The symbols $\triangle$, $\square$, $\diamond$, $\clubsuit$ represent four different integers from 1 to 9. Using the equations below, what is the value of $\square$?

$\triangle + \triangle + \triangle + \triangle + \triangle = \diamond$

$\triangle + \square + \square = \diamond$

$\square + \diamond = \clubsuit$

Guest Feb 25, 2021

#1**+2 **

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.**

CubeyThePenguin Feb 25, 2021

#2**+3 **

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 :)

MobiusLoops Feb 25, 2021