Someone shot 10 arrows at a target with 10 concentric rings, each being worth a different integer number of points from 1 to 10. How many different ways are there of scoring 10 points by doing this? (Note that not all the arrows have to hit the target and that order matters; 6 first then 4 is different from 4 first then 6. Also note that two or more arrows may hit the same ring.)

(In reply to Solution by David Shin)

David,  I got hopelessly lost trying to follow your logic (my problem not yours).  But I used a program (it ran for less than 1 second) that checked all the possibilities of 0-10 for each arrow and it agreed with your total of 92,378.  Well done for NOT using a computer program.

Posted by Nosher on 2004-09-21 18:01:00