2011=670*3+1+2+4+8-9-5

We have just welcomed the New Year, using all 10 digits and 4 basic arithmetic signs(+, -, /, and *).

Try to get 2011 with ALL 10 digits, significantly fewer signs and no brackets.

Hint: My solution uses 10 distinct digits and 3 signs only, but maybe a better solution exists.

(In reply to re(3): best I can do -- computer solutions involving multiplication by Charlie)

These operations are sequential, so if division is the second operation, imagine parentheses around the preceding addition or subtraction:

 10234 + 7865 / 9
 10235 + 7864 / 9
 10243 + 7856 / 9
 10246 + 7853 / 9
 10253 + 7846 / 9
 10256 + 7843 / 9
 10264 + 7835 / 9
 10265 + 7834 / 9
 102753 / 49 - 86
 10728 - 4695 / 3
 10834 + 7265 / 9
 10835 + 7264 / 9
 10843 + 7256 / 9
 10846 + 7253 / 9
 10853 + 7246 / 9
 10856 + 7243 / 9
 10864 + 7235 / 9
 10865 + 7234 / 9
 127 + 90368 / 45
 128 + 90367 / 45
 13920 - 5876 / 4
 14805 - 2739 / 6
 15027 - 6983 / 4
 167 + 90328 / 45
 168 + 90327 / 45
 1 + 742058 / 369
 18042 - 3965 / 7
 18360 / 4 - 2579
 18609 - 4532 / 7
 187065 - 42 / 93
 19350 - 7284 / 6
 19560 - 3472 / 8
 19740 - 3652 / 8
 20457 - 8391 / 6
 20739 - 4651 / 8
 20931 - 6854 / 7
 21063 - 4975 / 8
 23145 - 9068 / 7
 24051 - 7963 / 8
 25806 / 17 + 493
 28506 / 3 - 7491
 29451 / 3 - 7806
 296058 / 147 - 3
 30789 - 624 / 15
 327 + 90168 / 45
 328 + 90167 / 45
 34689 - 502 / 17
 35049 - 862 / 17
 35208 / 4 - 6791
 35402 + 796 / 18
 35406 + 792 / 18
 35492 + 706 / 18
 35496 + 702 / 18
 35702 + 496 / 18
 35706 + 492 / 18
 35792 + 406 / 18
 35796 + 402 / 18
 367 + 90128 / 45
 368 + 90127 / 45
 38160 / 4 - 7529
 38520 / 4 - 7619
 401 + 53896 / 27
 402 + 35796 / 18
 406 + 35792 / 18
 406 + 53891 / 27
 43098 / 6 - 5172
 43620 / 15 - 897
 45087 / 19 - 362
 4620 / 35 + 1879
 47109 - 856 / 23
 47823 / 19 - 506
 47850 / 29 + 361
 48720 / 35 + 619
 491 + 53806 / 27
 492 + 35706 / 18
 496 + 35702 / 18
 496 + 53801 / 27
 502 + 71894 / 36
 5046 / 29 + 1837
 504 + 71892 / 36
 50976 / 32 + 418
 53401 + 896 / 27
 53406 + 891 / 27
 53491 + 806 / 27
 53496 + 801 / 27
 53801 + 496 / 27
 53806 + 491 / 27
 53891 + 406 / 27
 53896 + 401 / 27
 56817 / 9 - 4302
 586074 / 291 - 3
 592 + 71804 / 36
 594 + 71802 / 36
 6042 / 53 + 1897
 61908 / 42 + 537
 62517 / 39 + 408
 68901 - 527 / 34
 702 + 35496 / 18
 70623 / 59 + 814
 706 + 35492 / 18
 71502 + 894 / 36
 71504 + 892 / 36
 71592 + 804 / 36
 71594 + 802 / 36
 71802 + 594 / 36
 71804 + 592 / 36
 71892 + 504 / 36
 71894 + 502 / 36
 7234 + 10865 / 9
 7235 + 10864 / 9
 7243 + 10856 / 9
 7246 + 10853 / 9
 7253 + 10846 / 9
 72531 / 9 - 6048
 7256 + 10843 / 9
 7264 + 10835 / 9
 7265 + 10834 / 9
 742051 + 8 / 369
 742058 + 1 / 369
 75609 / 31 - 428
 76908 / 34 - 251
 7834 + 10265 / 9
 7835 + 10264 / 9
 7843 + 10256 / 9
 7846 + 10253 / 9
 7853 + 10246 / 9
 7856 + 10243 / 9
 7864 + 10235 / 9
 7865 + 10234 / 9
 792 + 35406 / 18
 796 + 35402 / 18
 801 + 53496 / 27
 802 + 71594 / 36
 804 + 71592 / 36
 8064 / 32 + 1759
 806 + 53491 / 27
 80712 / 59 + 643
 87210 / 54 + 396
 8 + 742051 / 369
 891 + 53406 / 27
 892 + 71504 / 36
 894 + 71502 / 36
 896 + 53401 / 27
 90127 + 368 / 45
 90128 + 367 / 45
 90167 + 328 / 45
 90168 + 327 / 45
 90327 + 168 / 45
 90328 + 167 / 45
 90367 + 128 / 45
 90368 + 127 / 45
 907863 / 451 - 2

Posted by Charlie on 2011-01-01 14:45:42