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Super Ken (Posted on 2011-03-03)

The numbers 1 through 25 are arranged in a 5x5 array.

The product of the numbers in the first row is 483840.
The product of the numbers in the second row is 604032.
The product of the numbers in the third row is 90440.
The product of the numbers in the fourth row is 57960.

The product of the numbers in the first column is 193375.
The product of the numbers in the second column is 1530144.
The product of the numbers in the third column is 288000.
The product of the numbers in the fourth column is 258552.

What is the arrangement of the array?

See The Solution Submitted by Charlie

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Solution

Comment 2 of 2 |

7 | 24 | 20 | 18 | 8 ----+----+----+----+---- 13 | 22 | 16 | 12 | 11 ----+----+----+----+---- 17 | 14 | 10 | 19 | 2 ----+----+----+----+---- 5 | 23 | 6 | 21 | 4 ----+----+----+----+---- 25 | 9 | 15 | 3 | 1 By factoring each of the products one can find the row-column of the primes that are unique in the factorization of the numbers 1 to 25: 13, 17, 19, 23. As the prime factor 11 only exists twice in the set of factors for 1 to 25, and product of the second row has 2 factors of 11, one easily deduces that both 11 and 22 are in the second row. Cross-referencing the common factors one can readily deduce the first column's numbers, and whittle down the possibilities for the other rows and columns...eventually producing the arrangement as asked for.

Posted by Dej Mar on 2011-03-04 17:14:31

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