Hints and solutions to
Problem of the day for Friday, December 16

What is the next number in this sequence?

3, 7, 16, 32, 57, 93, ____

• This one becomes easy if you look at the differences between consecutive numbers in the sequence.
• 7 - 3 = 4, then 16 - 7 = 9, and then 32 - 16 = 16, and 57 - 32 = 25, and 93 - 57 = 36.
• So it looks like the differences are just the consecutive perfect squares. The next difference should thus be 7² = 49, and that will make the next number in the sequence equal to 93 + 49 = 142.

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