The understood Venn diagram is of 3 circles overlapping each other to form 7 enclosed regions.
Consider this structure being imposed upon the "Olympic Rings" to create 15 regions.
Place one number from 1 to 15 in each region so that the middle top ring (
Black) has a total of
Z + 2 while the other 4 total
Z each.
Ring Values:1. A B F G [Z]
2. B C D G H I J K [Z+2] (Black)
3. D E K L [Z]
4. F G H I M N [Z]
5. I J K L N O [Z]
Note: Olympic Rings has fewer overlaps.
(In reply to
re: Solution by Penny)
Why can't that be right?
The number is divisible by 2, as each solution has a reverse.
There's no need for the number to be divisible by 9 as there may be a different number of solutions for different totals.
Was there another criterion for saying the number is impossible?

Posted by Charlie
on 20080609 12:20:00 