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by ttv » Fri Jan 04, 2008 2:20 pm
In a certain game, each player scores either 2 points or 5 points. if n players score 2 points and m player score 5 points, and the total number of points scored is 50, what is the least possible positive difference between n and m ?
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by cris » Fri Jan 04, 2008 3:12 pm
is it 3?
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by Tud » Fri Jan 04, 2008 3:20 pm
I agree with 3.
2+5=7
50/7=7 remainder 1
Since nothing gets you 1 point you need to take something away. By removing 2 of the 2 pointers you add up to 45, then add 1 5 pointer to get to 50.

7-2=5 2pointers
7+1=8 5pointers.

8-5=3
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by Auzbee » Sat Jan 05, 2008 12:33 am
To crack this problem, since the point denominations are in 2 and 5, the LCM is 10. Hence the 2's will be in multiple of 5 and 5's in multiple of 2.
Least difference between n and m will be
8 of 5's - 5 of 2's = 3
If you take the next level it becomes:
6 of 5's - 10 of 2's = 4
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