Question 7

Anita wants to enter a number into each small triangular cell of the triangular table. The sum of the numbers in any two such cells with a common side must be the same. She has already entered two numbers. What is the sum of all the numbers in the table?

Solution

The triangular cells form a connected bipartite pattern, so cells of one alternating class have the same value and cells of the other class have the other value. The two given cells with values $$3$$ and $$2$$ belong to the same class, and there are four cells in each class. Hence the total is $$4\times3+4\times2=20$$.

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Anita wants to enter a number into each small triangular cell of the triangular table. The sum of the numbers in any two such cells with a common side must be the same. She has already entered two numbers. What is the sum of all the numbers in the table?

Solution

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