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Dart Discharge (Posted on 2013-11-07) Difficulty: 3 of 5
Three men - Art, Ben and Cal, played a dart game.
  1. Each dart that lodged in the game board scored 1, 5, 10, 25, 50 or 100 points.
  2. Each man threw nine darts that lodged in the board.
  3. Each man's total score was the same as any other man's total score.
  4. No number of points scored by a dart was scored by more than one man.
  5. Art scored all the 5s and Ben scored all the 10s.
Who scored all the 100s?

See The Solution Submitted by K Sengupta    
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Logical solution. Comment 2 of 2 |
I made an (obviously faulty) assumption at each man got two different scores. 
This quickly leads to no solutions because B would have to have all the 10's and 25's.   The attainable scores are 105, 135, 165, 195.
None of these can be attained by C who either has 1's and 50's or 1's and 100's.

It is true that since A has the 5's, the person with the 1's has exactly 5 of them and the third person has the 25's.  The total will end in 5.

Since someone has all of the same dart it is either 5's or 25's.  Only the option of 9*25=225 is possible.  This must be Cal.
So Ben has the five 1's with his at least one 10.  He can't reach 225 unless he has some high point darts:  at most 3 other darts (50's or 100's.)

Clearly the answer is that Ben has the 100's.
Specifically he has 5*1 + 2*10 + 2*100 = 225

This leaves Art with 5's and 50's.  It is readily apparent that
5*5 + 4*50 = 225.

  Posted by Jer on 2013-11-07 15:32:49
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