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Code to Zero

Find all 3 digit numbers such that by adding the first digit, the square of the second and the cube of the third you get the original number, for example 1 + 3^2 + 5^3 = 135.

Basic Rhythms

Explore a number pattern which has the same symmetries in different bases.

Learn about Number Bases

We are used to writing numbers in base ten, using 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Eg. 75 means 7 tens and five units. This article explains how numbers can be written in any number base.

Binary Squares

Age 16 to 18
Challenge Level

Is there a general pattern of $1$'s and $0$'s in a binary number which is the square of a binary number containing only $1$'s? Try squares of $11$, $111$, $1111$ etc? To generalize you might use the fact that the sum of powers of two is a geometric series.