TAKE
+ HOME
------
  EXAM

Given each alphabet is a digit, what are the possible solutions ?

(Don't scroll down if you want to give it a shot)





























Haskell in GHCI:

[(t,a,k,e,h,o,m,x)|t <- [0..9], a <- [0..9], k <- [0..9], e <- [0..9], h <- [0..9], o <- [0..9], m <- [0..9], x <- [0..9], (t*1000+a*100+k*10+e) + (h*1000+o*100+m*10+e) == e*1000+x*100+a*10+m, not (elem t [a,k,e,h,o,m,x]), not (elem a [k,e,h,o,m,x]), not (elem k [e,h,o,m,x]), not (elem e [h,o,m,x]), not (elem h [o,m,x]), not (elem o [m,x]), not (m==x)]

Alternatively, a much faster version (in a main.hs for example):

module Main where
main :: IO ()
main = putStrLn (show 
    [ (t,a,k,e,h,o,m,x)
    | t <- [0..9],
      a <- remove t [0..9],
      k <- remove' [t,a] [0..9],
      e <- remove' [t,a,k] [0..9],
      h <- remove' [t,a,k,e] [0..9],
      o <- remove' [t,a,k,e,h] [0..9],
      m <- remove' [t,a,k,e,h,o] [0..9],
      x <- remove' [t,a,k,e,h,o,m] [0..9],
      (t*1000+a*100+k*10+e) + (h*1000+o*100+m*10+e) == e*1000+x*100+a*10+m
    ])
    
-- remove an element once from the list
remove :: (Eq a) => a -> [a] -> [a]
remove _ [] = []
remove a (x:xs)
    | a == x = xs
    | otherwise = [x] ++ (remove a xs)
    
-- remove each element in the removal list once from the target list
remove' ::  (Eq a) => [a] -> [a] -> [a]
remove' _ [] = []
remove' [] xs = xs
remove' (a:as) bs = remove' as (remove a bs)

124 possible solutions:

T,A,K,E,H,O,M,X
0,4,1,6,5,9,2,3
0,5,7,4,3,6,8,2
0,5,9,3,2,8,6,4
0,7,1,3,2,8,6,5
0,7,3,2,1,8,4,5
0,7,3,2,1,9,4,6
0,9,1,4,3,6,8,5
0,9,1,4,3,7,8,6
0,9,2,8,7,4,6,3
0,9,2,8,7,5,6,4
0,9,5,2,1,7,4,6
0,9,5,2,1,8,4,7
1,0,2,4,3,5,8,6
1,0,2,4,3,6,8,7
1,0,3,8,7,4,6,5
1,0,4,3,2,7,6,8
1,0,4,3,2,8,6,9
1,0,5,7,6,2,4,3
1,0,5,7,6,8,4,9
1,0,7,6,5,3,2,4
1,0,7,6,5,8,2,9
1,2,5,8,7,0,6,3
1,3,0,6,5,4,2,7
1,3,2,5,4,6,0,9
1,3,4,9,7,6,8,0
1,3,5,4,2,6,8,0
1,3,8,7,5,6,4,0
1,3,8,7,6,5,4,9
1,4,8,3,2,0,6,5
1,5,0,7,6,3,4,8
1,5,6,9,7,4,8,0
1,5,7,4,3,0,8,6
1,7,3,2,0,8,4,5
1,7,3,2,0,9,4,6
1,7,6,5,4,2,0,9
1,7,9,4,2,5,8,3
1,8,3,7,5,2,4,0
1,8,5,6,4,9,2,7
1,8,7,5,3,4,0,2
1,8,7,5,3,6,0,4
1,9,5,2,0,7,4,6
1,9,5,2,0,8,4,7
1,9,8,5,3,7,0,6
2,0,1,9,7,3,8,4
2,0,1,9,7,4,8,5
2,0,1,9,7,5,8,6
2,0,4,3,1,7,6,8
2,0,4,3,1,8,6,9
2,3,4,9,6,7,8,1
2,3,4,9,7,1,8,5
2,3,5,4,1,6,8,0
2,4,5,9,7,1,8,6
2,4,8,3,1,0,6,5
2,5,9,3,0,8,6,4
2,6,1,7,5,3,4,9
2,7,0,8,5,4,6,1
2,7,1,3,0,8,6,5
2,7,6,5,3,1,0,8
2,7,9,4,1,5,8,3
2,8,3,7,5,1,4,9
2,8,7,5,3,1,0,9
3,0,1,9,6,4,8,5
3,0,2,4,1,5,8,6
3,0,2,4,1,6,8,7
3,1,2,9,6,5,8,7
3,1,4,8,5,0,6,2
3,1,4,8,5,7,6,9
3,2,5,8,4,7,6,0
3,4,5,9,6,2,8,7
3,5,7,4,0,6,8,2
3,5,7,4,1,0,8,6
3,6,7,9,5,4,8,1
3,7,0,8,4,5,6,2
3,7,0,8,5,2,6,9
3,7,6,5,2,1,0,8
3,8,7,5,1,4,0,2
3,8,7,5,1,6,0,4
3,8,7,5,2,1,0,9
3,9,1,4,0,6,8,5
3,9,1,4,0,7,8,6
3,9,2,8,4,1,6,0
3,9,8,5,1,7,0,6
4,0,1,9,5,2,8,3
4,0,1,9,5,6,8,7
4,2,5,8,3,7,6,0
4,3,2,5,1,6,0,9
4,7,0,8,3,5,6,2
4,7,6,5,1,2,0,9
4,8,5,6,1,9,2,7
4,9,2,8,3,1,6,0
5,0,1,9,4,2,8,3
5,0,1,9,4,6,8,7
5,0,7,6,1,3,2,4
5,0,7,6,1,8,2,9
5,1,4,8,3,0,6,2
5,1,4,8,3,7,6,9
5,3,0,6,1,4,2,7
5,3,8,7,1,6,4,0
5,4,1,6,0,9,2,3
5,6,1,7,2,3,4,9
5,6,7,9,3,4,8,1
5,7,0,8,2,4,6,1
5,7,0,8,3,2,6,9
5,8,3,7,1,2,4,0
5,8,3,7,2,1,4,9
6,0,1,9,3,4,8,5
6,0,5,7,1,2,4,3
6,0,5,7,1,8,4,9
6,1,2,9,3,5,8,7
6,3,4,9,2,7,8,1
6,3,8,7,1,5,4,9
6,4,5,9,3,2,8,7
6,5,0,7,1,3,4,8
7,0,1,9,2,3,8,4
7,0,1,9,2,4,8,5
7,0,1,9,2,5,8,6
7,0,3,8,1,4,6,5
7,2,5,8,1,0,6,3
7,3,4,9,1,6,8,0
7,3,4,9,2,1,8,5
7,4,5,9,2,1,8,6
7,5,6,9,1,4,8,0
7,9,2,8,0,4,6,3
7,9,2,8,0,5,6,4

... in response to a 6th grader's home work assignment :)