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 3 equal products (Posted on 2018-11-21)
Lets take a number 12 as an example . It can be partitoned into three integer summands in 12 ways:
12=1+1+10
12=1+2+9
12=1+3+8
12=1+4+7
12=1+5+6
12=2+2+8
12=2+3+7
12=2+4+6
12=2+5+5
12=3+3+6
12=3+4+5
12=4+4+4

Multiplying the 3 members of each partitions results in 12 distinct numbers: 10,18,...60,64.

On the other hand the same treatment applied to number 13 produces a pair of equal results: 13=1+6+6=2+2+9 and 1*6*6=2*2*9=36 (a well known problem of children's ages).

Find the smallest number which has 3 distinct partitions into 3 parts, each of them with the same product.

Bonus: list all numbers below 1000 boasting this feature.

 No Solution Yet Submitted by Ady TZIDON No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): Answer to the bonus. | Comment 6 of 10 |
(In reply to re: Answer to the bonus. by Ady TZIDON)

The process slows down considerably as the numbers get larger; I'll see how high I can go.

I've modified my bonus answer to show * placeholders for numbers below 102 that meet the criterion, making it easier to see.

 Posted by Charlie on 2018-11-22 15:07:47

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