## 1000.11 – Three Shapes, Three Numbers

Examine the grid below. Each shape represents a different number. The sum of each row is given in the rightmost column, and the sum of each column is given in the bottom row. What value does each shape represent? Solution

Make a copy of the blank grid and fill in the numbers for the shapes as you find them.

Here's one way to do it.

We first give the triangle, square, and pentagon letters to represent their values. We will call them $t$, $s$, and $p$ respectively. Next, notice that the second column is very similar to the third row. From the second column, we gather that $t+p+p+p=32$, while the third row tells us that $t+p+p=27$. This means $p = 5$. How obvious!

Now turn to the second row, where we have $s+p+p=18$. We can substitute what we know to get $s+10=18$, meaning that $s=8$.

Now that we have the value of all of our shapes but one, there are several ways to find the last. The fastest is to use the third row, where we have $t+p+p=27$. We can substitute to find $t+10=27$ so that $t = 17$.

Here is the final table: 