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Problem of the Week

Problem C

Branching Out

Consider the following number tree.

The first row of the tree has the number 0. The second row of the tree has the numbers 1 and 2. The third row has the numbers 3, 4, 5, and 6. The fourth row has the numbers 7, 8, 9, 10, 11, 12, 13, and 14. This pattern continues.

In this number tree, the integers greater than or equal to 0 are written out in increasing order, with the top row containing one integer and every row after containing twice as many integers as the row above it.

If row 1 contains the integer 0, what is the fifth number in row 10?

Themes: Algebra, Computational Thinking