A simple dart-board has three areas with scores of 1,4 and 7. If you throw up to four darts, what is the smallest total score that cannot be made?

Question

Whoever does this is the smartest in the world!!!!

Answer 1

This is not just logic; this is counting.

 

First, assume that all 4 darts might not hit the board, so each may score either 0, 1, 4, or 7.  Then, check what total scores are possible so that you can determine the lowest total score that is NOT possible with UP TO four darts.

 

# of 7's   # of 4's    # of 1's    Total Score

     0           0             0             0
     0           0             1             1
     0           0             2             2
     0           0             3             3
     0           0             4             4
     0           1             0             4
     0           1             1             5
     0           1             2             6
     0           1             3             7
     0           2             0             8
     0           2             1             9
     0           2             2             10
     0           3             0             12
     0           3             1             13
     0           4             0             16
     1           0             0             7
     1           0             1             8
     1           0             2             9
     1           0             3             10
     1           1             0             11
     1           1             1             12
     1           1             2             13
     1           2             0             15
     1           2             1             16
     1           3             0             19
     2           0             0             14
     2           0             1             15
     2           0             2             16
     2           1             0             18
     2           1             1             19
     2           2             0             22
     3           0             0             21
     3           0             1             22
     3           1             0             25
     4           0             0             28

 

Notice how the number of 7's, 4's, and 1's works like a "index counter" (like a gas pump or an odometer) and only includes values whose sum is "up to 4."  The total score does not include scores of 17, 20, 23, 24, 26, and 27 because it is NOT POSSIBLE to get them.

 

The lowest score that you cannot get is 17.

Answer 2

This is a logic question.

 

The lowest score one dart can make is 1, due to the score area on the board.  Suppose you were to score 1 point for all 4 darts.  Your total score would be 4.  Suppose all 4 darts do not hit any of the targets.  Then your lowest total score would be 0.  However, there is a chance that one dart will hit a target.  Therefore, zero is the lowest score that cannot be made.

 

 

Lowest possible score is 1, if one dart hits the 1 mark and the others miss.

Highest possible score is 28, if all four darts hit the 7 mark.

 

 

Does this make sense?