Always a multiple?

Source: nrich
Take a two digit number. Reverse the digits and add the result to your original number. Your answer is multiple of 11.
Prove that the answer will be a multiple of 11 for any starting number.
Will this work with three digit numbers? Four digit numbers? \(n\) digit numbers?

Show answer & extension


Show me a random puzzle
 Most recent collections 

Advent calendar 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

List of all puzzles


probability partitions division graphs logic star numbers trigonometry dominos median chocolate percentages regular shapes people maths time rugby prime numbers integers cryptic crossnumbers arrows range advent sport balancing remainders books number ave multiples complex numbers crossnumber combinatorics menace shape squares bases sums spheres square numbers dodecagons angles perfect numbers surds scales circles routes quadratics perimeter parabolas christmas numbers symmetry gerrymandering wordplay money irreducible numbers digital clocks clocks triangles multiplication pascal's triangle polygons speed addition floors dates crosswords cryptic clues the only crossnumber cube numbers coins products 2d shapes quadrilaterals triangle numbers doubling algebra digits hexagons factorials grids folding tube maps colouring means sum to infinity dice chalkdust crossnumber taxicab geometry cards shapes functions lines rectangles palindromes factors fractions chess sequences geometry volume planes area mean odd numbers probabilty proportion averages elections coordinates integration tiling square roots indices calculus crossnumbers ellipses differentiation unit fractions 3d shapes games


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021