Q: What is the longest sum of consecutive positive integers that sum to 2025?

A: The longest is 54 numbers from 11 til 64 (including 11 and 64).
If we add 11 and 64, we get 75.
The adjacent numbers to 11 and 64 that also add up to 75 like 12 and 63.
There are 27 pairs of numbers that add up to 75 — all those numbers sum to 2025.

Solution to December 2024 Brain Puzzler

Solution to November 2024 Brain Puzzler

Q: Which option is larger? No calculators please!

a) the sum of all cubes from 100 to 200

b) the sum of all squares from 1 to 100

squares are the numbers 1^2, 2^2 etc and cubes are 1^3, 2^3 etc

A: The squares.
The only cube from 100 to 200 is 125

But the squares from 1 to 100 include 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385 so the sum of the squares is larger.

Q: There are two ducks in front of two ducks, two ducks behind two ducks and two ducks in between. What is the minimum number of ducks?

A: 4 ducks