$\def\pm{{ ‰}} \def\pmf{{ ‰ \phantom.}} \def\pmm{{ ‰ \! ‰}} \def\pmmf{{ ‰ \! ‰ \phantom\%}} \DeclareMathOperator{\antilog}{antilog} \DeclareMathOperator{\arcsec}{arcsec} \DeclareMathOperator{\csch}{csch} \DeclareMathOperator{\arsinh}{arsinh} \DeclareMathOperator{\arcosh}{arcosh}$

## Integermania!

#### Four Fours

Four fours is a classic problem, dating back at least 90 years. Create each of the positive integers using four copies of 4, and any standard operations. All four numbers must be used, but no others. Your solutions will be assigned an exquisiteness level.

Use the online submissions page to get your Integermania solutions posted here!  This problem is now in semi-retired status, so you may submit an unlimited number of solutions each month.

 401 (2.4) $\dfrac{4 \times 4 + 4\%}{4\%}$ Dave Jones, 9/07Coventry, England 402 (3.4) $\dfrac{4}{4\%} \times 4 + \sqrt{4}$ Steve Wilson, 2/08Raytown, MO 403 (3.8) $(4 + 4)!\% - \dfrac{.4}{\sqrt{4}}$ Steve Wilson, 9/08Raytown, MO 404 (2.2) $4 \times \dfrac{4}{4\%} + 4$ Dave Jones, 12/06Coventry, England 405 (3.2) $\dfrac{4 - .4}{(.\overline{4} + .\overline{4})\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 406 (3.6) $\dfrac{4 \times 4 + 4!\%}{4\%}$ Steve Wilson, 6/08Raytown, MO 407 (3.8) $(4 + 4)!\% - \sqrt{4\%} + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 408 (3.4) $4 \times 4! \times 4 + 4!$ Steve Wilson, 6/08Raytown, MO 409 (3.2) $\dfrac{4 \times .\overline{4} + 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 6/08Martina Franca, Italy 410 (2.4) $\dfrac{4 \times 4 + .4}{4\%}$ Dave Jones, 9/07Coventry, England 411 (4.8) $\dfrac{\sqrt{4} - \sqrt{.\overline{4}\%}}{.\overline{4}\%} - 4!$ Steve Wilson, 10/08Raytown, MO 412 (3.8) $\dfrac{4 + 4 + 4!\%}{(\sqrt{4})\%}$ Steve Wilson, 12/08Raytown, MO 413 (5.0) $\coth\ln\coth\arsinh(4 \times 4) - \dfrac{4}{4\%}$ Steve Wilson, 9/23Lawrence, KS 414 (3.8) $\sqrt{\left(\sqrt{4^{4!}}\right)\%} + 4.4$ Steve Wilson, 11/23Lawrence, KS 415 (3.8) $\dfrac{\dfrac{4}{.4} - 4\%}{4! \pmf}$ Paolo Pellegrini, 8/08Martina Franca, Italy 416 (2.2) $4 \times \left(4 + \dfrac{4}{4\%} \right)$ Dave Jones, 3/07Coventry, England 417 (4.2) $\dfrac{\sqrt{4} - 4\%}{.\overline{4}\%} - 4!$ Paolo Pellegrini, 8/08Martina Franca, Italy 418 (4.0) $\dfrac{\sqrt{4}}{.\overline{4}\%} - \sqrt[.4]{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 419 (4.8) $\dfrac{4! + 4 - \sqrt{.\overline{4}\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 420 (3.2) $444 - 4!$ Steve Wilson, 2/08Raytown, MO 421 (4.8) $\dfrac{4! + 4 + \sqrt{.\overline{4}\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 11/08Raytown, MO 422 (4.0) $\dfrac{\sqrt{4}}{.\overline{4}\%} - 4! - 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 423 (4.4) $\dfrac{4! + 4 + \sqrt{4\%}}{\sqrt{.\overline{4}\%}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 424 (3.4) $\dfrac{4}{4\%} \times 4 + 4!$ Steve Wilson, 2/08Raytown, MO 425 (3.8) $\dfrac{ \dfrac{4}{4\%} + \sqrt{4}}{4!\%}$ Steve Wilson, 8/09Raytown, MO 426 (4.0) $\dfrac{4}{.\overline{4}\% \times \sqrt{4}} - 4!$ Paolo Pellegrini, 8/08Martina Franca, Italy 427 (4.0) $(4 + 4)!\% - \sqrt{4\%} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 428 (4.2) $\dfrac{\sqrt{4}}{.\overline{4}\%} - 4! + \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 429 (4.4) $\dfrac{\sqrt{4} - \sqrt{4\%}}{.\overline{4}\%} + 4!$ Paolo Pellegrini, 10/08Martina Franca, Italy 430 (3.8) $\dfrac{\sqrt{4} - (4! + 4)\%}{4 \pmf}$ Paolo Pellegrini, 8/08Martina Franca, Italy 431 (4.6) $\dfrac{\sqrt{4} - \sqrt{.\overline{4}\%}}{.\overline{4}\%} - 4$ Steve Wilson, 10/08Raytown, MO 432 (3.4) $4! \times (4 \times 4 + \sqrt{4})$ Paolo Pellegrini, 8/08Martina Franca, Italy 433 (4.8) $\dfrac{\sqrt{4} - \sqrt{.\overline{4}\%}}{.\overline{4}\%} - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 434 (3.8) $\dfrac{\sqrt{4}}{.\overline{4}\%} - 4 \times 4$ Steve Wilson, 6/08Raytown, MO 435 (4.0) $\dfrac{\sqrt{4} - (4! + \sqrt{4})\%}{4 \pmf}$ Paolo Pellegrini, 8/08Martina Franca, Italy 436 (3.2) $\dfrac{4}{.\overline{4}\%} \times (4\% + .\overline{4})$ Paolo Pellegrini, 8/08Martina Franca, Italy 437 (4.0) $\dfrac{\sqrt{4} - 4\%}{.\overline{4}\%} - 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 438 (4.2) $\dfrac{\sqrt{4}}{.\overline{4}\%} - \dfrac{4!}{\sqrt{4}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 439 (4.0) $\dfrac{\sqrt{4} - (4! + .4)\%}{4 \pmf}$ Paolo Pellegrini, 8/08Martina Franca, Italy 440 (2.0) $444 - 4$ Kimberly Grosdidier, 12/05Overland Park, KS 441 (3.8) $\dfrac{ \sqrt{(4 + \sqrt{4\%})^4}}{4\%}$ Paolo Pellegrini, 8/08Martina Franca, Italy 442 (3.2) $444 - \sqrt{4}$ Eric Millard, 5/07Olathe, KS 443 (4.2) $\dfrac{\sqrt{4} - 4\%}{.\overline{4}\%} + \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 444 (3.2) $.\overline{4} \times \dfrac{4}{.4\%} - .\overline{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 445 (4.0) $\dfrac{ \sqrt{4} - 4\%}{.\overline{4}\%} + 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 446 (3.0) $\dfrac{4}{(.\overline{4} + .\overline{4})\%} - 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 447 (4.4) $\dfrac{\sqrt{4} + .\overline{4}\%}{.\overline{4}\%} - 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 448 (2.0) $444 + 4$ Steven Charlton, 1/05Sunderland, England 449 (3.8) $\dfrac{\sqrt{4}}{.\overline{4}\%} - \dfrac44$ Steve Wilson, 6/08Raytown, MO 450 (2.6) $\dfrac{4 + 4}{4 \times .\overline{4}\%}$ Dave Jones, 1/08Coventry, England 451 (3.8) $\dfrac{\sqrt{4}}{.\overline{4}\%} + \dfrac44$ Steve Wilson, 6/08Raytown, MO 452 (3.8) $\dfrac{\sqrt{4}}{4 \pmf} - 4! - 4!$ Steve Wilson, 6/08Raytown, MO 453 (4.4) $\dfrac{\sqrt{4} - .\overline{4}\%}{.\overline{4}\%} + 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 454 (3.0) $\dfrac{4}{(.\overline{4} + .\overline{4})\%} + 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 455 (4.0) $\dfrac{\sqrt{4} + 4\%}{.\overline{4}\%} - 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 456 (3.4) $\dfrac{\sqrt{4}}{4 \pmf} - 44$ Steve Wilson, 6/08Raytown, MO 457 (4.0) $(\sqrt{4} + 4!)^4 \pmf + 4!\pmf$ Paolo Pellegrini, 8/08Martina Franca, Italy 458 (3.8) $\dfrac{\sqrt{4}}{.\overline{4}\%} + 4 + 4$ Steve Wilson, 6/08Raytown, MO 459 (4.0) $\dfrac{4 - \sqrt{4} + 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 8/08Martina Franca, Italy 460 (3.2) $\dfrac{4 \times .4 + .\overline{4}}{.\overline{4}\%}$ Paolo Pellegrini, 8/08Martina Franca, Italy 461 (4.2) $\dfrac{\sqrt{4} + 4\%}{.\overline{4}\%} + \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 462 (4.2) $\dfrac{\sqrt{4}}{.\overline{4}\%} + \dfrac{4!}{\sqrt{4}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 463 (4.0) $\dfrac{\sqrt{4} + 4\%}{.\overline{4}\%} + 4$ Paolo Pellegrini, 8/08Martina Franca, Italy 464 (3.4) $(4^4 - 4!) \times \sqrt{4}$ Paolo Pellegrini, 8/08Martina Franca, Italy 465 (4.2) $\dfrac{\sqrt{4} - 4\%}{.\overline{4}\%} + 4!$ Paolo Pellegrini, 8/08Martina Franca, Italy 466 (3.8) $\dfrac{\sqrt{4}}{.\overline{4}\%} + 4 \times 4$ Steve Wilson, 6/08Raytown, MO 467 (4.8) $\dfrac{\sqrt{4} + \sqrt{.\overline{4}\%}}{.\overline{4}\%} + \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 468 (3.2) $444 + 4!$ Steve Wilson, 2/08Raytown, MO 469 (4.6) $\dfrac{\sqrt{4} + \sqrt{.\overline{4}\%}}{.\overline{4}\%} + 4$ Steve Wilson, 10/08Raytown, MO 470 (3.8) $\dfrac{4 \times 4! - \sqrt{4}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 471 (4.2) $\dfrac{\sqrt{4} - \sqrt{4\%\%}}{4 \pmf} - 4!$ Paolo Pellegrini, 8/08Martina Franca, Italy 472 (3.6) $\dfrac{\sqrt{4}}{4 \pmf} - 4! - 4$ Steve Wilson, 6/08Raytown, MO 473 (4.8) $\cosh(4 \times \arcosh\sqrt{4 + 4}) + 4!$ Steve Wilson, 9/23Lawrence, KS 474 (3.8) $\dfrac{\sqrt{4}}{4 \pmf} - 4! - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 475 (3.4) $\dfrac{.4 + .\overline{4}}{.4 \times .\overline{4}\%}$ Paolo Pellegrini, 8/08Martina Franca, Italy 476 (3.4) $4! \times (4! - 4) - 4$ Steve Wilson, 6/08Raytown, MO 477 (3.8) $\dfrac{\sqrt{4} + 4 \pmf}{4 \pmf} - 4!$ Paolo Pellegrini, 8/08Martina Franca, Italy 478 (3.6) $4! \times (4! - 4) - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 479 (4.0) $\dfrac{4 \times 4! - \sqrt{4\%}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 480 (3.2) $4 \times \left(4 + \dfrac44 \right)!$ Steve Wilson, 10/08Raytown, MO 481 (4.0) $\dfrac{4 \times 4! + \sqrt{4\%}}{\sqrt{4\%}}$ Paolo Pellegrini, 8/08Martina Franca, Italy 482 (3.6) $4! \times (4! - 4) + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 483 (4.2) $\dfrac{\sqrt{4} + 4\%}{.\overline{4}\%} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 484 (3.4) $4! \times (4! - 4) + 4$ Steve Wilson, 6/08Raytown, MO 485 (3.8) $\dfrac{\sqrt{4} - (4 + \sqrt{4})\%}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 486 (3.6) $\dfrac{\sqrt{4} - 4\%}{4 \pmf} - 4$ Steve Wilson, 6/08Raytown, MO 487 (4.8) $\cosh(\sqrt{4} \times \arcosh(4 \times 4)) - 4!$ Steve Wilson, 9/23Lawrence, KS 488 (3.4) $4^4 \times \sqrt{4} - 4!$ Steve Wilson, 10/08Raytown, MO 489 (3.6) $\dfrac{\sqrt{4} - 44 \pmf}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 490 (3.2) $\dfrac{4 \times .\overline{4} + .4}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 491 (3.8) $\dfrac{\sqrt{4}}{4 \pmf} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 6/08Raytown, MO 492 (3.4) $\dfrac{\sqrt{4}}{4 \pmf} - 4 - 4$ Steve Wilson, 6/08Raytown, MO 493 (3.8) $\dfrac{\sqrt{4} - (4! + 4)\pmf}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 494 (3.6) $\dfrac{\sqrt{4}}{4 \pmf} - 4 - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 495 (2.8) $\dfrac{4 - 4\%}{(.4 + .4)\%}$ Steve Wilson, 10/08Raytown, MO 496 (2.6) $\dfrac{4}{(.4 + .4)\%} - 4$ Dave Jones, 1/08Coventry, England 497 (3.6) $\dfrac{\sqrt{4} + 4 \pmf}{4 \pmf} - 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 498 (3.4) $\dfrac{4}{(4 + 4)\pmf} - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 499 (3.4) $\dfrac{\sqrt{4}}{4 \pmf} - \dfrac44$ Steve Wilson, 6/08Raytown, MO 500 (2.2) $\dfrac{4 \times 4 + 4}{4\%}$ Dave Jones, 9/06Coventry, England 501 (3.4) $\dfrac{\sqrt{4}}{4 \pmf} + \dfrac44$ Steve Wilson, 6/08Raytown, MO 502 (3.4) $\dfrac{4}{(4 + 4)\pmf} + \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 503 (3.6) $\dfrac{\sqrt{4} - 4 \pmf}{4 \pmf} + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 504 (2.6) $\dfrac{4}{(.4 + .4)\%} + 4$ Dave Jones, 1/08Coventry, England 505 (2.8) $\dfrac{4 + 4\%}{(.4 + .4)\%}$ Steve Wilson, 10/08Raytown, MO 506 (3.6) $\dfrac{\sqrt{4}}{4 \pmf} + 4 + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 507 (3.8) $\dfrac{\sqrt{4} + (4! + 4)\pmf}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 508 (3.2) $4^4 \times \sqrt{4} - 4$ Jeremy Miller, 9/07Olathe, KS 509 (3.8) $\dfrac{\sqrt{4}}{4 \pmf} + \dfrac{4}{.\overline{4}}$ Steve Wilson, 6/08Raytown, MO 510 (3.4) $4^4 \times \sqrt{4} - \sqrt{4}$ Steve Wilson, 9/08Raytown, MO 511 (3.6) $\dfrac{\sqrt{4} + 44 \pmf}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 512 (3.0) $4^4 + 4^4$ Josh Brown, 6/04Lawrence, KS 513 (3.8) $\dfrac{\sqrt[\sqrt{4\%}]{4} + \sqrt{4}}{\sqrt{4}}$ Paolo Pellegrini, 9/08Martina Franca, Italy 514 (3.4) $4^4 \times \sqrt{4} + \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 515 (3.8) $\dfrac{\sqrt{4} + (4 + \sqrt{4})\%}{4 \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 516 (3.2) $4^4 \times \sqrt{4} + 4$ Jeremy Miller, 9/07Olathe, KS 517 (4.6) $\cosh(\sqrt{4} \times \arsinh(4 \times 4)) + 4$ Steve Wilson, 9/23Lawrence, KS 518 (4.0) $\dfrac{\sqrt{4} - 4! \pmf}{4 \pmf} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 519 (4.2) $\dfrac{\sqrt{4} - \sqrt{4\%\%}}{4 \pmf} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 520 (3.2) $(4^4 + 4) \times \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 521 (4.8) $\coth\ln\coth\arsinh(4 \times 4) + 4 + 4$ Steve Wilson, 9/23Lawrence, KS 522 (3.8) $\dfrac{\sqrt{4}}{4 \pmf} + 4! - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 523 (3.8) $\dfrac{\sqrt{4} - 4\pmf}{4 \pmf} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 524 (3.4) $\dfrac{4}{(4 + 4)\pmf} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 525 (3.6) $\dfrac{\sqrt{4} + \dfrac{.4}{4}}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 526 (3.8) $\dfrac{\sqrt{4}}{4 \pmf} + 4! + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 527 (4.8) $\coth\ln\coth\arcosh(4 \times 4) + 4 \times 4$ Steve Wilson, 9/23Lawrence, KS 528 (3.4) $44 \times \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 10/08Raytown, MO 529 (3.4) $\sqrt{\left(4! - \dfrac44 \right)^4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 530 (3.8) $(4! - \sqrt{4}) \times 4! + \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 531 (4.2) $\dfrac{\sqrt{4} + .4 - 4\%}{.\overline{4}\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 532 (3.4) $4! \times 4! - 44$ Steve Wilson, 6/08Raytown, MO 533 (4.4) $\dfrac{(4! - .4)\%}{.\overline{4}\pmf} + \sqrt{4}$ Steve Wilson, 10/23Lawrence, KS 534 (3.8) $\dfrac{\sqrt{4} + 4\%}{4 \pmf} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 535 (4.4) $\sqrt{4\%^{-4}} - \dfrac{.4}{.\overline{4}\%}$ Steve Wilson, 12/08Raytown, MO 536 (3.4) $4^4 \times \sqrt{4} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 537 (4.6) $\dfrac{4!\%}{.\overline{4} \pmf} - \sqrt{\dfrac{4}{.\overline{4}}}$ Steve Wilson, 8/09Raytown, MO 538 (4.2) $\dfrac{\sqrt{4} + .4}{.\overline{4}\%} - \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 539 (4.0) $\dfrac{4!\%}{.\overline{4} \pmf} - \dfrac44$ Paolo Pellegrini, 8/09Martina Franca, Italy 540 (2.8) $\dfrac{4 - 4 \times .4}{.\overline{4}\%}$ Dave Jones, 12/07Coventry, England 541 (4.0) $\dfrac{4!\%}{.\overline{4} \pmf} + \dfrac44$ Steve Wilson, 8/09Raytown, MO 542 (4.2) $\dfrac{\sqrt{4} + .4}{.\overline{4}\%} + \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 543 (4.6) $\dfrac{4!\%}{.\overline{4} \pmf} + \sqrt{\dfrac{4}{.\overline{4}}}$ Steve Wilson, 8/09Raytown, MO 544 (3.4) $\dfrac{\sqrt{4}}{4 \pmf} + 44$ Steve Wilson, 6/08Raytown, MO 545 (4.0) $\dfrac{4! - \sqrt{4} - \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 546 (3.6) $\dfrac{4! - \sqrt{4}}{4\%} - 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 547 (4.4) $\dfrac{(4! + .4)\%}{.\overline{4}\pmf} - \sqrt{4}$ Steve Wilson, 10/23Lawrence, KS 548 (3.6) $4! \times 4! - 4! - 4$ Steve Wilson, 6/08Raytown, MO 549 (3.8) $\dfrac{4! - \sqrt{4} - 4\%}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 550 (2.2) $\dfrac{44}{(4 + 4)\%}$ Dave Jones, 9/07Coventry, England 551 (3.8) $\dfrac{4! - \sqrt{4} + 4\%}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 552 (3.4) $4! \times \left(4! - \dfrac44 \right)$ Steve Wilson, 6/08Raytown, MO 553 (4.2) $\dfrac{(4! + .4)\%}{.\overline{4}\pmf} + 4$ Steve Wilson, 10/23Lawrence, KS 554 (3.6) $\dfrac{4! - \sqrt{4}}{4\%} + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 555 (4.0) $\dfrac{4! - \sqrt{4} + \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 556 (3.2) $\dfrac{.\overline{4}}{(4+4)\%\%} + .\overline{4}$ Steve Wilson, 10/08Raytown, MO 557 (3.8) $\sqrt{(4! - .4)^4} + 4\%$ Paolo Pellegrini, 9/08Martina Franca, Italy 558 (4.0) $\dfrac{\sqrt{4} + 4!\%}{4 \pmf} - \sqrt{4}$ Steve Wilson, 8/09Raytown, MO 559 (4.0) $\dfrac{\sqrt{4} + (4! - .4)\%}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 560 (3.4) $(4! - 4) \times (4! + 4)$ Steve Wilson, 6/08Raytown, MO 561 (4.0) $\dfrac{\sqrt{4} + (4! + .4)\%}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 562 (4.0) $\dfrac{\sqrt{4} + 4!\%}{4 \pmf} + \sqrt{4}$ Steve Wilson, 8/09Raytown, MO 563 (4.8) $\dfrac{4!\% - .\overline{4}\pmf}{.\overline{4}\pmf} + 4!$ Steve Wilson, 10/23Lawrence, KS 564 (3.6) $4! \times \left(4! - \dfrac{\sqrt{4}}{4} \right)$ Paolo Pellegrini, 9/08Martina Franca, Italy 565 (4.0) $\dfrac{\sqrt{4} + (4! + \sqrt{4})\%}{4 \pmf}$ Paolo Pellegrini, 9/08Martina Franca, Italy 566 (3.6) $4! \times 4! - \dfrac{4}{.4}$ Steve Wilson, 6/08Raytown, MO 567 (3.4) $\dfrac{4^4 - 4}{.\overline{4}}$ Steve Wilson, 10/08Raytown, MO 568 (3.4) $4! \times 4! - 4 - 4$ Steve Wilson, 6/08Raytown, MO 569 (5.2) $4! \times 4! - 4 - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 570 (3.6) $4! \times 4! - 4 - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 571 (3.8) $4! \times 4! - \dfrac{\sqrt{4}}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 572 (3.4) $\dfrac{4^4}{.\overline{4}} - 4$ Steve Wilson, 10/08Raytown, MO 573 (4.0) $4! \times 4! - \sqrt{\dfrac{4}{.\overline{4}}}$ Paolo Pellegrini, 9/08Martina Franca, Italy 574 (3.6) $4! \times 4! - 4 + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 575 (3.4) $4! \times 4! - \dfrac44$ Steve Wilson, 6/08Raytown, MO 576 (3.2) $\sqrt[4]{4!^{4+4}}$ Steve Wilson, 5/11Raytown, MO 577 (3.4) $4! \times 4! + \dfrac44$ Steve Wilson, 6/08Raytown, MO 578 (3.6) $4! \times 4! + 4 - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 579 (4.0) $4! \times 4! + \sqrt{\dfrac{4}{.\overline{4}}}$ Paolo Pellegrini, 9/08Martina Franca, Italy 580 (3.4) $\dfrac{4^4}{.\overline{4}} + 4$ Steve Wilson, 10/08Raytown, MO 581 (3.6) $\sqrt{ 4\%^{-4}} - 44$ Steve Wilson, 10/08Raytown, MO 582 (3.6) $4! \times 4! + 4 + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 583 (4.4) $\dfrac{(4! + \sqrt{4})\%}{.\overline{4}\pmf} - \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 584 (3.4) $4! \times 4! + 4 + 4$ "mathwhiz", 1/07Newton, MA 585 (3.4) $\dfrac{4^4 + 4}{.\overline{4}}$ Steve Wilson, 10/08Raytown, MO 586 (3.6) $4! \times 4! + \dfrac{4}{.4}$ Steve Wilson, 6/08Raytown, MO 587 (4.4) $\dfrac{(4! + \sqrt{4})\%}{.\overline{4}\pmf} + \sqrt{4}$ Steve Wilson, 11/23Lawrence, KS 588 (3.6) $4! \times \left( 4! + \dfrac{\sqrt{4}}{4} \right)$ Paolo Pellegrini, 9/08Martina Franca, Italy 589 (3.6) $\dfrac{4! - .44}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 590 (3.6) $\dfrac{4!}{4\%} - \dfrac{4}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 591 (3.8) $\dfrac{4!}{4\%} - \dfrac{4}{.\overline{4}}$ Steve Wilson, 6/08Raytown, MO 592 (3.4) $\dfrac{4!}{4\%} - 4 - 4$ Steve Wilson, 2/08Raytown, MO 593 (3.8) $\dfrac{4! - (4! + 4)\%}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 594 (3.6) $\dfrac{4!}{4\%} - 4 - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 595 (3.6) $\dfrac{4! - 4\%}{4\%} - 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 596 (3.6) $4! \times 4! + 4! - 4$ Steve Wilson, 6/08Raytown, MO 597 (3.6) $\dfrac{4! + 4\%}{4\%} - 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 598 (3.6) $\dfrac{4!}{4\%} - 4 + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 599 (3.4) $\dfrac{4!}{4\%} - \dfrac44$ Steve Wilson, 6/08Raytown, MO 600 (2.6) $\dfrac{4 - 4 \times .4}{.4\%}$ Dave Jones, 12/07Coventry, England 601 (3.4) $\dfrac{4!}{4\%} + \dfrac44$ Steve Wilson, 6/08Raytown, MO 602 (3.6) $\dfrac{4!}{4\%} + 4 - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 603 (3.6) $\dfrac{4! - 4\%}{4\%} + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 604 (3.6) $4! \times 4! + 4! + 4$ Steve Wilson, 6/08Raytown, MO 605 (3.6) $\dfrac{4! + 4\%}{4\%} + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 606 (3.6) $\dfrac{4!}{4\%} + 4 + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 607 (3.8) $\dfrac{4! + (4! + 4)\%}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 608 (3.4) $\dfrac{4!}{4\%} + 4 + 4$ Steve Wilson, 2/08Raytown, MO 609 (3.6) $\sqrt{ 4\%^{-4}} - 4 \times 4$ Steve Wilson, 10/08Raytown, MO 610 (3.6) $\dfrac{4!}{4\%} + \dfrac{4}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 611 (3.6) $\dfrac{4! + .44}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 612 (3.8) $\dfrac{4!}{4\%} + \dfrac{4!}{\sqrt{4}}$ Paolo Pellegrini, 9/08Martina Franca, Italy 613 (4.0) $\sqrt{ 4\%^{-4}} - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 12/08Raytown, MO 614 (3.6) $\dfrac{4! + .4}{4\%} + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 615 (3.8) $\sqrt{ 4\%^{-4}} - \dfrac{4}{.4}$ Steve Wilson, 10/08Raytown, MO 616 (3.4) $\dfrac{4!}{4\%} + 4 \times 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 617 (3.6) $\sqrt{ 4\%^{-4}} - 4 - 4$ Steve Wilson, 10/08Raytown, MO 618 (3.8) $\dfrac{4! + (4 + \sqrt{4}) \pmf}{4\%}$ Paolo Pellegrini, 9/08Martina Franca, Italy 619 (3.8) $\sqrt{ 4\%^{-4}} - 4 - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 620 (3.4) $4! \times 4! + 44$ Steve Wilson, 6/08Raytown, MO 621 (3.4) $\left( \dfrac{\sqrt{4}}{.4} \right)^4 - 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 622 (3.8) $\dfrac{4!}{4\%} + 4! - \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 623 (3.6) $\left( \dfrac{\sqrt{4}}{.4} \right)^4 - \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 624 (3.6) $\sqrt{ 4\%^{-4}} - \dfrac44$ Steve Wilson, 10/08Raytown, MO 625 (2.4) $\dfrac{4}{4 \times 4\% \times 4\%}$ Dave Jones, 2/08Coventry, England 626 (3.6) $\sqrt{ 4\%^{-4}} + \dfrac44$ Steve Wilson, 10/08Raytown, MO 627 (3.6) $\left( \dfrac{\sqrt{4}}{.4} \right)^4 + \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 628 (3.6) $\dfrac{4!}{4\%} + 4! + 4$ Steve Wilson, 2/08Raytown, MO 629 (3.4) $\left( \dfrac{\sqrt{4}}{.4} \right)^4 + 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 630 (3.2) $\dfrac{4^4 - 4}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 631 (3.8) $\sqrt{ 4\%^{-4}} + 4 + \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 632 (3.6) $\dfrac{4!}{4\%} + \sqrt[.4]{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 633 (3.6) $\sqrt{ 4\%^{-4}} + 4 + 4$ Steve Wilson, 10/08Raytown, MO 634 (3.8) $\dfrac{4! + .4}{4\%} + 4!$ Paolo Pellegrini, 9/08Martina Franca, Italy 635 (3.4) $\dfrac{4^4 - \sqrt{4}}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 636 (3.2) $\dfrac{4^4}{.4} - 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 637 (4.0) $\sqrt{ 4\% ^{-4}} + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 12/08Raytown, MO 638 (3.4) $\dfrac{4^4}{.4} - \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 639 (3.4) $\dfrac{4^4 - .4}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 640 (3.4) $(4! - 4) \times \sqrt[.4]{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 641 (3.4) $\dfrac{4^4 + .4}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 642 (3.4) $\dfrac{4^4}{.4} + \sqrt{4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 643 (5.0) $\dfrac{4^4}{.4} + \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 644 (3.2) $\dfrac{4^4}{.4} + 4$ Steve Wilson, 10/08Raytown, MO 645 (3.4) $\dfrac{4^4 + \sqrt{4}}{.4}$ Paolo Pellegrini, 9/08Martina Franca, Italy 646 (3.6) $\dfrac{4! + \sqrt{4}}{4\%} - 4$ Paolo Pellegrini, 9/08Martina Franca, Italy 647 (4.0) $\sqrt{ 4\%^{-4}} + 4! - \sqrt{4}$ Steve Wilson, 12/08Raytown, MO 648 (3.6) $4! \times (4! + 4) - 4!$ Steve Wilson, 6/08Raytown, MO 649 (3.6) $\left( \dfrac{\sqrt{4}}{.4} \right)^4 + 4!$ Paolo Pellegrini, 10/08Martina Franca, Italy 650 (3.2) $\dfrac{4^4 + 4}{.4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 651 (3.8) $\dfrac{4! + \sqrt{4} + 4\%}{4\%}$ Paolo Pellegrini, 10/08Martina Franca, Italy 652 (3.8) $\dfrac{4! + \sqrt{4}}{4\%} + \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 653 (3.8) $\sqrt{ 4\%^{-4}} + 4! + 4$ Steve Wilson, 10/08Raytown, MO 654 (3.6) $\dfrac{4! + \sqrt{4}}{4\%} + 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 655 (4.0) $\dfrac{4! + \sqrt{4} + \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 10/08Martina Franca, Italy 656 (3.8) $\dfrac{44}{\sqrt{.\overline{4}\%}} - 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 657 (4.2) $\dfrac{44 - \sqrt{4\%}}{\sqrt{.\overline{4}\%}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 658 (4.0) $\dfrac{44}{\sqrt{.\overline{4}\%}} - \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 659 (4.6) $\dfrac{44 - \sqrt{.\overline{4}\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 10/08Raytown, MO 660 (3.6) $(4 - 4\%) \times \dfrac{4}{4! \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 661 (4.6) $\dfrac{44 + \sqrt{.\overline{4}\%}}{\sqrt{.\overline{4}\%}}$ Steve Wilson, 10/08Raytown, MO 662 (4.0) $\dfrac{44}{\sqrt{.\overline{4}\%}} + \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 663 (4.2) $\dfrac{44 + \sqrt{4\%}}{\sqrt{.\overline{4}\%}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 664 (3.4) $\dfrac{4^4}{.4} + 4!$ Paolo Pellegrini, 10/08Martina Franca, Italy 665 (3.6) $\dfrac{4 \times 4 - 4\%}{4! \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 666 (3.6) $(4 - 4\pmf) \times \dfrac{4}{4! \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 667 (3.8) $(4 + (\sqrt{4}) \pmf) \times \dfrac{4}{4! \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 668 (3.4) $4! \times (4! + 4) - 4$ Steve Wilson, 6/08Raytown, MO 669 (3.6) $\sqrt{ 4\%^{-4}} + 44$ Steve Wilson, 10/08Raytown, MO 670 (3.6) $4! \times (4! + 4) - \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 671 (3.8) $\dfrac{4!}{(4 - .\overline{4})\%} - 4$ Paolo Pellegrini, 8/09Martina Franca, Italy 672 (3.4) $4! \times (\sqrt[.4]{4} - 4)$ Paolo Pellegrini, 10/08Martina Franca, Italy 673 (4.0) $\sqrt{ 4\%^{-4}} + 4! + 4!$ Steve Wilson, 10/08Raytown, MO 674 (3.6) $4! \times (4! + 4) + \sqrt{4}$ Steve Wilson, 6/08Raytown, MO 675 (2.6) $\dfrac{4 - \dfrac44}{.\overline{4}\%}$ Dave Jones, 12/07Coventry, England 676 (3.4) $4! \times (4! + 4) + 4$ Steve Wilson, 6/08Raytown, MO 677 (4.0) $\dfrac{4!}{(4 - .\overline{4})\%} + \sqrt{4}$ Steve Wilson, 8/09Raytown, MO 678 (3.8) $\sqrt{(4! + \sqrt{4})^4} + \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 679 (3.8) $\dfrac{4!}{(4 - .\overline{4})\%} + 4$ Steve Wilson, 8/09Raytown, MO 680 (3.6) $\sqrt{(4! + \sqrt{4})^4} + 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 681 (5.4) $\sqrt{(4! + \sqrt{4})^4} + \cot\arctan \sqrt{4\%}$ Steve Wilson, 8/09Raytown, MO 682 (5.6) $\sqrt{(4! + \sqrt{4})^4} + \left( \coth\ln \sqrt{\sqrt{4}} \right)!$ Steve Wilson, 8/09Raytown, MO 683 (5.4) $\dfrac{ \coth\ln \sqrt{\sqrt{4}}}{.\overline{4}\%} + 4 + 4$ Steve Wilson, 8/09Raytown, MO 684 (4.0) $4! \times \left(4! + \dfrac{\sqrt{4}}{.\overline{4}} \right)$ Paolo Pellegrini, 10/08Martina Franca, Italy 685 (4.0) $\sqrt{ 4\%^{-4}} + \dfrac{4!}{.4}$ Steve Wilson, 10/08Raytown, MO 686 (4.2) $\dfrac{ \sqrt[\sqrt{.\overline{4}}]{\sqrt{4} - 4\%}}{4 \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 687 (5.8) $\dfrac{\coth\ln \sqrt{\sqrt{4}}}{.\overline{4}\%} + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 688 (3.6) $\left( \dfrac{4!}{4} \right)! - \sqrt[.4]{4}$ Steve Wilson, 10/08Raytown, MO 689 (4.4) $\sqrt{ 4\%^{-4}} + \sqrt{\sqrt{\sqrt{4^{4!}}}}$ Steve Wilson, 12/08Raytown, MO 690 (4.2) $\left( \dfrac{4!}{4} \right)! - \sqrt{ \dfrac{4}{.\overline{4}\%}}$ Steve Wilson, 10/08Raytown, MO 691 (5.4) $\dfrac{\coth\ln \sqrt{\sqrt{4}}}{.\overline{4}\%} + 4 \times 4$ Steve Wilson, 8/09Raytown, MO 692 (3.6) $\left( \dfrac{4!}{4} \right)! - 4! - 4$ Steve Wilson, 10/08Raytown, MO 693 (5.4) $\left( \dfrac{4!}{4} \right)! - 4! - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 694 (3.8) $\left( \dfrac{4!}{4} \right)! - 4! - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 695 (3.8) $\dfrac{4! + 4 - \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 10/08Martina Franca, Italy 696 (3.4) $\dfrac{4! + 4}{4\%} - 4$ Brad Anderson, 9/06Overland Park, KS 697 (5.2) $\dfrac{4! + 4}{4\%} - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 698 (3.6) $\dfrac{4! + 4}{4\%} - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 699 (3.6) $\dfrac{4! + 4 - 4\%}{4\%}$ Steve Wilson, 10/08Raytown, MO 700 (3.4) $\dfrac{4^4 + 4!}{.4}$ Steve Wilson, 10/08Raytown, MO 701 (3.6) $\dfrac{4! + 4 + 4\%}{4\%}$ Steve Wilson, 10/08Raytown, MO 702 (3.6) $\dfrac{4! + 4}{4\%} + \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 703 (5.2) $\dfrac{4! + 4}{4\%} + \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 704 (2.0) $4 \times 44 \times 4$ Tim Murphy, 5/03Olathe, KS 705 (3.8) $\dfrac{4! + 4 + \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 10/08Martina Franca, Italy 706 (3.8) $\dfrac{4! + 4 + 4!\%}{4\%}$ Steve Wilson, 10/08Raytown, MO 707 (5.8) $\left(\left( \coth\ln \sqrt{\sqrt{4}} \right)!\right)! - \dfrac{4! + \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 708 (3.8) $\left( \dfrac{4!}{4} \right)! - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 10/08Raytown, MO 709 (5.2) $\left(\left( \coth\ln \sqrt{\sqrt{4}} \right)!\right)! - \dfrac{44}{4}$ Steve Wilson, 8/09Raytown, MO 710 (3.2) $\dfrac{4 - .4 - .\overline{4}}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 711 (3.8) $\left( \dfrac{4!}{4} \right)! - \dfrac{4}{.\overline{4}}$ Steve Wilson, 10/08Raytown, MO 712 (3.4) $\left( \dfrac{4!}{4} \right)! - 4 - 4$ Steve Wilson, 10/08Raytown, MO 713 (5.2) $\left( \dfrac{4!}{4} \right)! - 4 - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 714 (3.6) $\left( \dfrac{4!}{4} \right)! - 4 - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 715 (3.8) $\left( \dfrac{4!}{4} \right)! - \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 10/08Raytown, MO 716 (3.4) $\left( \dfrac{4}{.4} - 4 \right)! - 4$ Steve Wilson, 10/08Raytown, MO 717 (4.0) $\left( \dfrac{4!}{4} \right)! - \sqrt{ \dfrac{4}{.\overline{4}}}$ Steve Wilson, 10/08Raytown, MO 718 (3.6) $\left( \dfrac{4}{.4} - 4 \right)! - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 719 (3.4) $\left( \dfrac{4!}{4} \right)! - \dfrac44$ Steve Wilson, 10/08Raytown, MO 720 (2.6) $\dfrac{4}{\left( \dfrac44 - .\overline{4} \right)\%}$ Steve Wilson, 10/08Raytown, MO 721 (3.4) $\left( \dfrac{4!}{4} \right)! + \dfrac44$ Steve Wilson, 10/08Raytown, MO 722 (3.6) $\left( \dfrac{4}{.4} - 4 \right)! + \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 723 (4.0) $\left( \dfrac{4!}{4} \right)! + \sqrt{ \dfrac{4}{.\overline{4}}}$ Steve Wilson, 10/08Raytown, MO 724 (3.4) $\left( \dfrac{4}{.4} - 4 \right)! + 4$ Steve Wilson, 10/08Raytown, MO 725 (3.8) $\left( \dfrac{4!}{4} \right)! + \dfrac{\sqrt{4}}{.4}$ Steve Wilson, 10/08Raytown, MO 726 (3.6) $\left( \dfrac{4!}{4} \right)! + 4 + \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 727 (5.2) $\left( \dfrac{4!}{4} \right)! + 4 + \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 728 (3.4) $\left( \dfrac{4!}{4} \right)! + 4 + 4$ Steve Wilson, 10/08Raytown, MO 729 (3.8) $\left( \dfrac{4!}{4} \right)! + \dfrac{4}{.\overline{4}}$ Steve Wilson, 10/08Raytown, MO 730 (3.6) $\left( \dfrac{4!}{4} \right)! + \dfrac{4}{.4}$ Steve Wilson, 10/08Raytown, MO 731 (5.2) $\left(\left( \coth\ln \sqrt{\sqrt{4}} \right)! \right)! + \dfrac{44}{4}$ Steve Wilson, 8/09Raytown, MO 732 (3.8) $\left( \dfrac{4!}{4} \right)! + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 10/08Raytown, MO 733 (5.8) $\left(\left( \coth\ln \sqrt{\sqrt{4}} \right)! \right)! + \dfrac{4! + \sqrt{4}}{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 734 (4.6) $\dfrac{4}{(\csch \ln 4)\%} - 4 \times 4$ Steve Wilson, 8/09Raytown, MO 735 (4.0) $\dfrac{ \sqrt{(4 + \sqrt{4\%})^4}}{4! \pmf}$ Paolo Pellegrini, 10/08Martina Franca, Italy 736 (3.4) $\left( \dfrac{4!}{4} \right)! + 4 \times 4$ Steve Wilson, 10/08Raytown, MO 737 (5.6) $\left(\left( \coth\ln \sqrt{\sqrt{4}} \right)! \right)! + 4 \times (4 + \cot\arctan 4)$ Steve Wilson, 8/09Raytown, MO 738 (5.0) $\dfrac{4}{(\csch \ln 4)\%} - \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 739 (5.2) $\dfrac{ \coth\ln \sqrt{\sqrt{4}} - 44 \pmf}{4 \pmf}$ Steve Wilson, 8/09Raytown, MO 740 (3.6) $\left( \dfrac{4!}{4} \right)! + 4! - 4$ Steve Wilson, 10/08Raytown, MO 741 (4.4) $\dfrac{\sqrt{4} - 4! \pmf}{4 \pmf \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 742 (3.8) $\left( \dfrac{4!}{4} \right)! + 4! - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 743 (5.4) $\left(\left( \coth\ln \sqrt{\sqrt{4}} \right)! \right)! + 4! - \dfrac44$ Steve Wilson, 8/09Raytown, MO 744 (3.2) $\dfrac{4}{4 \pmf} - 4^4$ Steve Wilson, 10/08Raytown, MO 745 (4.2) $\sqrt{ 4\%^{-4}} + \left( \dfrac{\sqrt{4}}{.4} \right)!$ Steve Wilson, 12/08Raytown, MO 746 (3.6) $\dfrac{4!}{(\sqrt[.4]{4}) \pmf} - 4$ Steve Wilson, 10/08Raytown, MO 747 (4.2) $\dfrac{ \dfrac{\sqrt{4}}{4 \pmf} - \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 748 (3.6) $\left( \dfrac{4!}{4} \right)! + 4! + 4$ Steve Wilson, 10/08Raytown, MO 749 (4.0) $\dfrac{ \dfrac{\sqrt{4}}{\left(\sqrt{.\overline{4}} \right)\pmf} - 4}{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 750 (2.4) $\dfrac{4 - \dfrac44}{.4\%}$ Dave Jones, 10/07Coventry, England 751 (4.0) $\dfrac{ \dfrac{\sqrt{4}}{\left( \sqrt{.\overline{4}} \right) \pmf} + 4}{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 752 (3.6) $\left( \dfrac{4!}{4} \right)! + \sqrt[.4]{4}$ Steve Wilson, 10/08Raytown, MO 753 (4.2) $\dfrac{\dfrac{\sqrt{4}}{4 \pmf} + \sqrt{4}}{\sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 754 (3.6) $\dfrac{4!}{(\sqrt[.4]{4}) \pmf} + 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 755 (5.4) $\dfrac{4!}{(\sqrt[.4]{4}) \pmf} + \cot\arctan \sqrt{4\%}$ Steve Wilson, 8/09Raytown, MO 756 (3.4) $\dfrac{\sqrt{4}}{4 \pmf} + 4^4$ Steve Wilson, 10/08Raytown, MO 757 (5.4) $\dfrac{4}{(\csch\ln 4)\%} + 4 + \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 758 (4.6) $\dfrac{4}{(\csch\ln 4)\%} + 4 + 4$ Steve Wilson, 8/09Raytown, MO 759 (4.4) $\dfrac{\sqrt{4} + 4! \pmf}{4 \pmf \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 760 (3.2) $\dfrac{.4 + .\overline{4}}{.\overline{4}\%} \times 4$ Steve Wilson, 10/08Raytown, MO 761 (5.2) $\dfrac{ \coth\ln \sqrt{\sqrt{4}} + 44 \pmf}{4 \pmf}$ Steve Wilson, 8/09Raytown, MO 762 (5.0) $\dfrac{4}{(\csch \ln 4)\%} + \dfrac{4!}{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 763 (5.2) $4! \times \sqrt[.4]{4} - \cot\arctan \sqrt{4\%}$ Steve Wilson, 8/09Raytown, MO 764 (3.4) $\left( \dfrac{4!}{4} \right)! + 44$ Steve Wilson, 10/08Raytown, MO 765 (4.2) $\dfrac{\sqrt{4} + 4\%}{4 \pmf \times \sqrt{.\overline{4}}}$ Paolo Pellegrini, 10/08Martina Franca, Italy 766 (3.6) $4! \times \sqrt[.4]{4} - \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 767 (5.2) $4! \times \sqrt[.4]{4} - \tan\arcsec \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 768 (3.2) $4! \times (4 + 4) \times 4$ Steve Wilson, 10/08Raytown, MO 769 (5.2) $4! \times \sqrt[.4]{4} + \tan\arcsec \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 770 (3.8) $\left( \dfrac{4!}{4} \right)! + \dfrac{\sqrt{4}}{4\%}$ Steve Wilson, 10/08Raytown, MO 771 (5.2) $4! \times \sqrt[.4]{4} + \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 772 (3.4) $4! \times \sqrt[.4]{4} + 4$ Steve Wilson, 10/08Raytown, MO 773 (5.2) $4! \times \sqrt[.4]{4} + \cot\arctan \sqrt{4\%}$ Steve Wilson, 8/09Raytown, MO 774 (3.8) $\dfrac{4!}{(\sqrt[.4]{4}) \pmf} + 4!$ Paolo Pellegrini, 10/08Martina Franca, Italy 775 (3.0) $\dfrac{4 - \dfrac{.4}{.\overline{4}}}{.4\%}$ Steve Wilson, 10/08Raytown, MO 776 (3.6) $\dfrac{\sqrt[.4]{4}}{4\%} - 4!$ Steve Wilson, 10/08Raytown, MO 777 (5.8) $\dfrac{\sqrt{4}}{(\cot\arctan 4)\%} - 4! + \tan\arcsec \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 778 (4.8) $\dfrac{4}{(\csch\ln 4)\%} + 4! + 4$ Steve Wilson, 8/09Raytown, MO 779 (5.2) $\sqrt{(4! + 4)^4} - \cot\arctan \sqrt{4\%}$ Steve Wilson, 8/09Raytown, MO 780 (3.8) $\left( \dfrac{4!}{4} \right)! + \dfrac{4!}{.4}$ Steve Wilson, 10/08Raytown, MO 781 (5.2) $\sqrt{(4! + 4)^4} - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 782 (3.6) $\sqrt{(4! + 4)^4} - \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 783 (5.2) $\sqrt{(4! + 4)^4} - \tan\arcsec\sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 784 (3.4) $(4! + 4) \times (4! + 4)$ Steve Wilson, 10/08Raytown, MO 785 (5.2) $\sqrt{(4! + 4)^4} + \tan\arcsec \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 786 (3.6) $\sqrt{(4! + 4)^4} + \sqrt{4}$ Paolo Pellegrini, 10/08Martina Franca, Italy 787 (5.2) $\sqrt{(4! + 4)^4} + \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 788 (3.4) $\sqrt{(4! + 4)^4} + 4$ Paolo Pellegrini, 10/08Martina Franca, Italy 789 (5.2) $\sqrt{(4! + 4)^4} + \cot\arctan \sqrt{4\%}$ Steve Wilson, 8/09Raytown, MO 790 (3.6) $\dfrac{\sqrt[.4]{4} - .4}{4\%}$ Steve Wilson, 10/08Raytown, MO 791 (3.2) $\dfrac{4 - .\overline{4} - 4\%}{.\overline{4}\%}$ Steve Wilson, 10/08Raytown, MO 792 (3.6) $4! \times \sqrt[.4]{4} + 4!$ Steve Wilson, 10/08Raytown, MO 793 (5.6) $\dfrac{\sqrt{4}}{(\cot\arctan 4)\%} - 4 - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 794 (4.6) $\dfrac{4}{(\csch \ln 4)\%} + 44$ Steve Wilson, 10/23Lawrence, KS 795 (3.8) $\dfrac{ \sqrt[.4]{4} - \sqrt{4\%}}{4\%}$ Paolo Pellegrini, 10/08Martina Franca, Italy 796 (3.0) $\dfrac{4 - .\overline{4}}{.\overline{4}\%} - 4$ Steve Wilson, 10/08Raytown, MO 797 (5.2) $4 \times \dfrac{4}{(\sqrt{4})\%} - \coth\ln \sqrt{\sqrt{4}}$ Steve Wilson, 8/09Raytown, MO 798 (3.6) $\dfrac{\sqrt[.4]{4}}{4\%} - \sqrt{4}$ Steve Wilson, 10/08Raytown, MO 799 (3.6) $\dfrac{ \sqrt[.4]{4} - 4\%}{4\%}$ Paolo Pellegrini, 10/08Martina Franca, Italy 800 (2.2) $(4 + 4) \times \dfrac{4}{4\%}$ Dave Jones, 3/07Coventry, England