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 Two top targets (Posted on 2013-09-06)
Find the two highest numbers consisting each of 6 DISTINCT digits such that each when divided by any of the numbers 7, 17, 66 leaves a remainder of 5?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 computer solution Comment 2 of 2 |

DEFDBL A-Z
FOR a = 1 TO 9
used(a) = 1
v1 = 100000 * a
FOR b = 0 TO 9
IF used(b) = 0 THEN
used(b) = 1
v2 = v1 + 10000 * b
FOR c = 0 TO 9
IF used(c) = 0 THEN
used(c) = 1
v3 = v2 + 1000 * c
FOR d = 0 TO 9
IF used(d) = 0 THEN
used(d) = 1
v4 = v3 + 100 * d
FOR e = 0 TO 9
IF used(e) = 0 THEN
used(e) = 1
v5 = v4 + 10 * e
FOR f = 0 TO 9
IF used(f) = 0 THEN
used(f) = 1
v6 = v5 + f

IF v6 MOD 7 = 5 THEN
IF v6 MOD 17 = 5 THEN
IF v6 MOD 66 = 5 THEN
PRINT v6
END IF
END IF
END IF

used(f) = 0
END IF
NEXT f
used(e) = 0
END IF
NEXT e
used(d) = 0
END IF
NEXT d
used(c) = 0
END IF
NEXT c
used(b) = 0
END IF
NEXT b
used(a) = 0
NEXT a

finds all solutions, not just the highest two:

180647
259187
267041
274895
298457
361289
392705
431975
486953
518369
620471
659741
746135
761843
824675
856091
863945
879653
895361
903215

but of course the highest two are the last two: 895361 and 903215.

 Posted by Charlie on 2013-09-06 12:10:14

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