The symbols $\triangle$, $\square$, $\diamond$, $\clubsuit$ represent four different integers from 1 to 9. Using the equations below, what is the value of $\square$?
$\triangle + \triangle + \triangle + \triangle + \triangle = \diamond$
$\triangle + \square + \square = \diamond$
$\square + \diamond = \clubsuit$
+1223 triangle = T, square = S, diamond = D, club = C
5T = D . (1)
T + 2S = D . (2)
S + D = C . (3)
Equations (1) and (2) are equal:
5T = T + 2S
4T = 2S
2T = S
Then we can look at equation (3):
S + T + 2S = C
7S/2 = C
Every symbol is an integer from 1 to 9, so S = 7.
+505 T=Triangle, D=Diamond, S=Square, and C=Clover
T+T+T+T+T=D
T can't be larger than 1 because D would be larger than 9.
So this means 1+1+1+1+1=5, which D=5
1+S+S=5
1+2S=5
2S=4
S=2
Square is equal to 2
S+D=C = 2+5=7, so C is equal to 7
T=1, D=5, S=2, C=7
I know CubeyThePenguin got a different answer, so I'm not sure if Cubey's or mine is correct :)
