June 2009
Problem of the Month
Missing Number Problem
William Jacob Bechem
in Games Magazine March 2009
There are ten positive integers less than 1000 that cannot be written as the sum of
consecutive natural numbers.
For example, 9 = 4 + 5, 10 = 1 + 2 + 3 + 4,
11 = 5 + 6, and 12 = 3 + 4 + 5.
The first two numbers that cannot be written as the sum of consecutive natural numbers are 1 and 2.
Can you find the other eight exceptions?
Solution to the Problem:
The answer is all the powers of 2:
1, 2, 4, 8, 16, 32, 64, 128, 256, 512.