Reverse bases

Find two digits \(a\) and \(b\) such that \(ab\) in base 10 is equal to \(ba\) in base 4.
Find two digits \(c\) and \(d\) such that \(cd\) in base 10 is equal to \(dc\) in base 7.
Find two digits \(e\) and \(f\) such that \(ef\) in base 9 is equal to \(fe\) in base 5.

Show answer & extension

Tags: numbers, bases
If you enjoyed this puzzle, check out Sunday Afternoon Maths VII,
puzzles about bases, or a random puzzle.


Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020