716 would seem to be the desired answer.
10 for N=1 to 999999999
20 Cu=N*N*N
30 Ct6=0
40 S$=str(Cu)
50 for I=1 to len(S$)
60 if mid(S$,I,1)="6" then inc Ct6
70 next
80 if Ct6>=4 then print N,Cu,Ct6:inc Pct
81 if Pct>40 then cancel for:end
90 next
finds the first 41 that have four or five sixes:
n n^3 number of
sixes
716 367061696 4
806 523606616 4
874 667627624 4
982 946966168 4
989 967361669 4
1185 1664006625 4
1188 1676676672 5
1332 2363266368 4
1378 2616662152 4
1387 2668267603 4
1456 3086626816 4
1466 3150662696 4
1786 5696975656 4
1841 6239666321 4
1863 6466042647 4
1882 6665900968 4
2054 8665653464 4
2201 10662526601 4
2286 11946169656 4
2306 12262468616 4
2331 12665630691 4
2385 13566416625 4
2521 16022066761 4
2523 16060229667 4
2536 16309766656 5
2553 16639966377 4
2556 16698695616 5
2786 21624363656 4
2907 24566036643 4
2954 25776946664 4
2966 26092364696 4
2986 26623761256 4
3306 36133376616 4
3323 36693659267 4
3438 40636623672 4
3454 41206620664 4
3556 44966103616 4
3606 46889669016 4
3821 55786756661 4
3832 56269946368 4
3863 57646656647 5
A little tweaking of the program shows the lowest for the given number of sixes in the cube:
4 64 1
36 46656 3
716 367061696 4
1188 1676676672 5
4055 66676466375 6
13832 2646396666368 7
18821 6666963601661 8
190806 6946660616126616 9
1542023 3666676156163166167 10
3971816 62656677666653866496 11
13881356 2674826866666660366016 12
55009989 166465666639716668628669 13
154057624 3656365366626065666266624 14
The 2 entry is missing as no number under 36 has a cube with two 6's. The first cube with exactly two sixes is 55^3 = 166375.
Of course we can also get smaller and smaller numbers with exactly four sixes, so there is no smallest:
-716 -367061696 4
-806 -523606616 4
-874 -667627624 4
-982 -946966168 4
-989 -967361669 4
-1185 -1664006625 4
-1332 -2363266368 4
-1378 -2616662152 4
-1387 -2668267603 4
-1456 -3086626816 4
-1466 -3150662696 4
-1786 -5696975656 4
-1841 -6239666321 4
-1863 -6466042647 4
-1882 -6665900968 4
-2054 -8665653464 4
-2201 -10662526601 4
-2286 -11946169656 4
-2306 -12262468616 4
-2331 -12665630691 4
-2385 -13566416625 4
-2521 -16022066761 4
-2523 -16060229667 4
-2553 -16639966377 4
-2786 -21624363656 4
-2907 -24566036643 4
-2954 -25776946664 4
-2966 -26092364696 4
-2986 -26623761256 4
-3306 -36133376616 4
-3323 -36693659267 4
-3438 -40636623672 4
-3454 -41206620664 4
-3556 -44966103616 4
-3606 -46889669016 4
-3821 -55786756661 4
-3832 -56269946368 4
-3883 -58546666387 4
-3896 -59136667136 4
-3941 -61209566621 4
-3951 -61676694351 4
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Posted by Charlie
on 2013-03-05 13:56:51 |
computer solution
