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# algebra

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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\$

Feb 25, 2021

#1
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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.

Feb 25, 2021
#2
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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 :)

Feb 25, 2021