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Mission impossible (Posted on 2013-04-03) Difficulty: 2 of 5
In a certain football contest the winner scores 3 points, the loser 0, and in the case of a draw each team scores 1 point.

Out of all "possible" final scores (0<R<3*n) for a team, participating in N games, how many final results cannot be achieved?

See The Solution Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Not achieved (spoiler)......hinting | Comment 3 of 5 |
(In reply to re: Not achieved (spoiler)......hinting by Ady TZIDON)

I believe my solution is correct.  Lets say N=4.  There are 13 "possible" final scores {0,1,...12} but one of them cannot be achieved.

Result One way to achieve it in W-L-D format
0 0-4-0
1 0-3-1
2 0-2-2
3 1-3-0
4 1-2-1
5 1-1-2
6 2-2-0
7 2-1-1
8 2-0-2
9 3-1-0
10 3-0-1
11 not possible
12 4-0-0

Note the pattern in the D column.  11 points by this pattern requires 3-(-1)-2 but you can't have a negative number of losses.



  Posted by Jer on 2013-04-03 13:23:24

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