Re: math and logic problem

On 9/29/2007 1:32 PM, Rainer Rosenthal wrote:
Michael Harrington wrote:
"Michael Harrington" <mikharr@xxxxxxxxxxx> wrote
"conrad" <conrad@xxxxxxxxxx> wrote
I recently came across a puzzle
which asked to utilize all
nine numerals, 1-9, in
some arrangement so as to produce
a fraction that equals 1/3.

The solution is 5832/17496.

How should a problem like this
be attacked?

One way would be by an exhaustive computer
program. ...

2 Solutions found 5823/17469
5832/17496

Yes and they are the only ones for abcd/efghi = 1/3.

I checked all 4-digit numbers abcd. That's only 3024 many,
namely 4! * binom(9,4) = 3024. It must only be tested
whether 3*abcd has the appropriate form efghi.

If I haven't made any mistakes, here is a complete list of permutations of the nine non-zero numerals such that the last five digits is an integral multiple of the first four digits:


6729/13458 = 1/2
6792/13584 = 1/2
6927/13854 = 1/2
7269/14538 = 1/2
7293/14586 = 1/2
7329/14658 = 1/2
7692/15384 = 1/2
7923/15846 = 1/2
7932/15864 = 1/2
9267/18534 = 1/2
9273/18546 = 1/2
9327/18654 = 1/2
5823/17469 = 1/3
5832/17496 = 1/3
3942/15768 = 1/4
4392/17568 = 1/4
5796/23184 = 1/4
7956/31824 = 1/4
2697/13485 = 1/5
2769/13845 = 1/5
2937/14685 = 1/5
2967/14835 = 1/5
2973/14865 = 1/5
3297/16485 = 1/5
3729/18645 = 1/5
6297/31485 = 1/5
7629/38145 = 1/5
9237/46185 = 1/5
9627/48135 = 1/5
9723/48615 = 1/5
2943/17658 = 1/6
4653/27918 = 1/6
5697/34182 = 1/6
2394/16758 = 1/7
2637/18459 = 1/7
4527/31689 = 1/7
5274/36918 = 1/7
5418/37926 = 1/7
5976/41832 = 1/7
7614/53298 = 1/7
3187/25496 = 1/8
4589/36712 = 1/8
4591/36728 = 1/8
4689/37512 = 1/8
4691/37528 = 1/8
4769/38152 = 1/8
5237/41896 = 1/8
5371/42968 = 1/8
5789/46312 = 1/8
5791/46328 = 1/8
5839/46712 = 1/8
5892/47136 = 1/8
5916/47328 = 1/8
5921/47368 = 1/8
6479/51832 = 1/8
6741/53928 = 1/8
6789/54312 = 1/8
6791/54328 = 1/8
6839/54712 = 1/8
7123/56984 = 1/8
7312/58496 = 1/8
7364/58912 = 1/8
7416/59328 = 1/8
7421/59368 = 1/8
7894/63152 = 1/8
7941/63528 = 1/8
8174/65392 = 1/8
8179/65432 = 1/8
8394/67152 = 1/8
8419/67352 = 1/8
8439/67512 = 1/8
8932/71456 = 1/8
8942/71536 = 1/8
8953/71624 = 1/8
8954/71632 = 1/8
9156/73248 = 1/8
9158/73264 = 1/8
9182/73456 = 1/8
9316/74528 = 1/8
9321/74568 = 1/8
9352/74816 = 1/8
9416/75328 = 1/8
9421/75368 = 1/8
9523/76184 = 1/8
9531/76248 = 1/8
9541/76328 = 1/8
6381/57429 = 1/9
6471/58239 = 1/9
8361/75249 = 1/9
3816/45792 = 1/12
6129/73548 = 1/12
7461/89532 = 1/12
7632/91584 = 1/12
5184/67392 = 1/13
6273/81549 = 1/13
7281/94653 = 1/13
1839/25746 = 1/14
1956/27384 = 1/14
2967/41538 = 1/14
3297/46158 = 1/14
3678/51492 = 1/14
3912/54768 = 1/14
4398/61572 = 1/14
4713/65982 = 1/14
1863/27945 = 1/15
6183/92745 = 1/15
2871/45936 = 1/16
4581/73296 = 1/16
6147/98352 = 1/16
1579/26843 = 1/17
1679/28543 = 1/17
1738/29546 = 1/17
2174/36958 = 1/17
2689/45713 = 1/17
2693/45781 = 1/17
3217/54689 = 1/17
3478/59126 = 1/17
3821/64957 = 1/17
3841/65297 = 1/17
3952/67184 = 1/17
3954/67218 = 1/17
4519/76823 = 1/17
4523/76891 = 1/17
4596/78132 = 1/17
4619/78523 = 1/17
4623/78591 = 1/17
4796/81532 = 1/17
4916/83572 = 1/17
4921/83657 = 1/17
5261/89437 = 1/17
5263/89471 = 1/17
5273/89641 = 1/17
5378/91426 = 1/17
5461/92837 = 1/17
5463/92871 = 1/17
5478/93126 = 1/17
1593/28674 = 1/18
2736/51984 = 1/19
4293/81567 = 1/19
2349/51678 = 1/22
1578/36294 = 1/23
3549/81627 = 1/23
3564/81972 = 1/23
1647/39528 = 1/24
1953/46872 = 1/24
1653/42978 = 1/26
2173/56498 = 1/26
2379/61854 = 1/26
2589/67314 = 1/26
2593/67418 = 1/26
2943/76518 = 1/26
3179/82654 = 1/26
3451/89726 = 1/26
3571/92846 = 1/26
1476/39852 = 1/27
1836/49572 = 1/27
2583/69741 = 1/27
3582/96714 = 1/27
2691/75348 = 1/28
1296/37584 = 1/29
2541/73689 = 1/29
2349/75168 = 1/32
1379/48265 = 1/35
1827/63945 = 1/35
1837/64295 = 1/35
2139/74865 = 1/35
2671/93485 = 1/35
1782/65934 = 1/37
1734/65892 = 1/38
1956/74328 = 1/38
2178/93654 = 1/43
1329/58476 = 1/44
1347/59268 = 1/44
1543/67892 = 1/44
1578/69432 = 1/44
2167/95348 = 1/44
1269/58374 = 1/46
1836/95472 = 1/52
1243/65879 = 1/53
1432/75896 = 1/53
1592/84376 = 1/53
1746/92538 = 1/53
1254/73986 = 1/59
1283/79546 = 1/62
1528/94736 = 1/62
1269/83754 = 1/66
1452/98736 = 1/68

--Mark

.

Relevant Pages

  • Re: math and logic problem
    ... some arrangement so as to produce ... a fraction that equals 1/3. ...
    (sci.math)
  • Re: math and logic problem
    ... some arrangement so as to produce ... a fraction that equals 1/3. ...
    (sci.math)
  • Re: math and logic problem
    ... some arrangement so as to produce ... a fraction that equals 1/3. ...
    (sci.math)
  • Re: math and logic problem
    ... a fraction that equals 1/3. ... of the nine non-zero numerals such that the last five digits is an ... integral multiple of the first four digits: ... I can confirm your list as it equals my list. ...
    (sci.math)
  • math and logic problem
    ... some arrangement so as to produce ... a fraction that equals 1/3. ...
    (sci.math)
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