mscroggs.co.uk
mscroggs.co.uk

subscribe

Advent calendar 2019

22 December

In bases 3 to 9, the number 112 is: \(11011_3\), \(1300_4\), \(422_5\), \(304_6\), \(220_7\), \(160_8\), and \(134_9\). In bases 3, 4, 6, 8 and 9, these representations contain no digit 2.
There are two 3-digit numbers that contain no 2 in their representations in all the bases between 3 and 9 (inclusive). Today's number is the smaller of these two numbers.

Show answer

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2025

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2026