# How many unique ways are there to achieve a score in Football? [duplicate]

Challenge: given a number, calculate how many unique, order-independent ways there are to achieve a score of that number in American Football.

Let's see how few characters can be used in each of your favorite languages! The usual rules apply. Input and output in a way that is natural to your language.

Recall that the ways to score in Football are safety (2 points), field goal (3 points), touchdown (6 points), touchdown + extra point (7 points), and touchdown + 2-point conversion (8 points).

For example, given 9 as input, the program should return 4, since you could score:

• 1 touchdown + extra point and 1 safety
• 1 touchdown and 1 field goal
• 3 field goals
• 3 safeties and 1 field goal

Note that order does not matter.

• I'm not familiar with American Football. Is the question just about ways of partitioning the number using 2,3,6,7 and 8? Commented Jan 6, 2014 at 22:35
• @swish yup! Just an actual version of the problem I found myself thinking about. Commented Jan 6, 2014 at 22:43
• This is essentially identical to Need change of 78 cents except for the values of some constants. (Although on reflection, since this question is better posed, it might be preferable to close the other one as a duplicate of this one). Commented Jan 6, 2014 at 23:48
• Awhh. I watch the Canadian Football League. I want my 1 point for punting into the endzone! Commented Jan 7, 2014 at 14:22

# Mathematica - 42

Length@IntegerPartitions[#,∞,{2,3,6,7,8}]&


# Prolog - 140

Never wrote anything in Prolog before, just knew that this problem should be quite nice for it.

p(0,_,[]).
p(N,[H|T],O):- N>=H,p(N,T,O).
p(N,[H|S],[H|T]):- N>=H,M is N-H,p(M,[H|S],T).
f(N,C):- aggregate(count,X^p(N,[2,3,6,7,8],X),C).

?- f(9,C).
C = 4.

• I only see 42 chars. Does this have something to do with the unicode character? Commented Jan 7, 2014 at 14:25
• @Cruncher Oh, I forgot to put f= at the start, so it would be a function definition. Commented Jan 7, 2014 at 15:23

## Python - 146

t=int(input())
from itertools import*
print len([a for a in chain(*(combinations_with_replacement([2,3,6,7,8],n) for n in range(t)))if sum(a)==t])

• Instead of from itertools import ..., you can use from itertools import*. You only use combinations_with_replacement once, so having to use it wouldn't cost you after this change.
– null
Commented Jan 7, 2014 at 13:19
• True, I'll change it, thanks! Commented Jan 7, 2014 at 14:05