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UKMT Pink Kangaroo, 2017

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Carlos wants to put numbers in the number pyramid shown in such a way that each number above the bottom row is the sum of the two numbers immediately below it. What is the largest number of odd numbers that Carlos could put in the pyramid?

(A) $13$ (B) $14$ (C) $15$ (D) $16$ (E) $17$

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