Question 20. In the following calculations, the same digits are hidden under the same figures. Different digits are hidden under different figures. Triangle plus triangle equals square, circle. Circle plus triangle equals square, square. What is the value of triangle times circle times square? Let's take a look at our first two equations. Triangle plus triangle equal to square, circle, and circle triangle equal to square, square. Let's focus on the first one. Now, we know that the triangle and triangle have to be the same digit, but their sum is two different digits. So this tells us one very important thing. This cannot be zero plus zero because that would equal to zero. And these triangles, while they can be zeros, square and circle cannot be zeros because those are different figures. So instead, we have to add two single digit numbers, for example, nine plus nine, and end up with a two digit number. Now, since nine and nine work, it could be any number from five to nine, since five plus five would equal ten. So the only thing we know for certain is that the square will contain one, and we can mark the other squares with one. Next, we have circle triangle. We can start guessing different numbers. We know that one will not be any of them, and we have to have the sum of 11 when we do circle plus triangle. For example, we could have two plus nine, three plus eight, four plus seven, or five plus six. All of these will give us an answer of 11. And all of these could also be flipped around. For example, nine plus two, eight plus three, seven plus four, and six plus five. However, in the top equation, we see that the circle is the second digit. This is important because the two triangles, any number multiplied by two or added to itself will always end with an even number. So the circle cannot be an odd number. So we can flip these all around, and these are our only possible solutions without flipping numbers around. So let's start trying these out. We put two for the circles and nine for the triangles. When we do this, two plus nine equals 11, but nine plus nine does not equal 12. So that will not be the answer. Next, let's try eight for the circles and threes for the triangles. This does not work because three plus three does not equal 18. Next, let's try fours. When we do seven plus seven, we get 14. And when we do four plus seven, we get 11. So that means that these numbers all work. So we'll do triangle times circle times square, which will be seven times four times one. Then we get our answer, which is d, 28.

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