 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  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 7 of 10 | I've now verified that  all the numbers up through 2000 that fail to boast the feature are 102 or less.

I've tried to make the comment on OEIS, but I've forgotten my password, and the temporary password they sent doesn't work. I'll try it again tomorrow.

BTW, the sequence for those that do meet the criterion is A119028.

Edited on November 22, 2018, 6:44 pm
 Posted by Charlie on 2018-11-22 18:42:00 Please log in:

 Search: Search body:
Forums (0)