Solution to "Three-digit numbers"

Share this page
May 1998

When we write a three-digit number in base-ten we are really saying "so many hundreds", "so many tens" and "so many units". If our number is n and the digits are represented by x, y and z (reading from left to right) then we can write:

n = 100x + 10y + z

We are told that

y = x + z


n = 100x + 10(x + z) + z

n = 110x + 11z

n = 11(10x + z)

therefore n must be divisible by 11!

  • Want facts and want them fast? Our Maths in a minute series explores key mathematical concepts in just a few words.

  • The BloodCounts! project is gearing up towards one of the largest-scale applications yet of machine learning in medicine and healthcare.

  • What do chocolate and mayonnaise have in common? It's maths! Find out how in this podcast featuring engineer Valerie Pinfield.

  • Is it possible to write unique music with the limited quantity of notes and chords available? We ask musician Oli Freke!

  • How can maths help to understand the Southern Ocean, a vital component of the Earth's climate system?

  • Was the mathematical modelling projecting the course of the pandemic too pessimistic, or were the projections justified? Matt Keeling tells our colleagues from SBIDER about the COVID models that fed into public policy.