# Puzzles

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#### Advent calendar 2017

#### Sunday afternoon maths LXII

What's the star?#### Sunday afternoon maths LXI

XYZ#### Sunday afternoon maths LX

Where is Evariste?Bending a straw

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## Tags

time geometry 2d shapes 3d shapes numbers spheres trigonometry complex numbers algebra lines graphs coordinates odd numbers fractions differentiation calculus folding tube maps ellipses triangle numbers money bases triangles squares area square numbers chess probability circles averages speed sport multiples dates factors parabolas functions logic cards games people maths shape prime numbers irreducible numbers probabilty angles proportion dice integration sum to infinity dodecagons hexagons multiplication factorials coins shapes regular shapes colouring grids floors integers rugby crosswords percentages digits sums christmas rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices planes volume number partitions ave pascal's triangle mean advent symmetry arrows addition cube numbers star numbers perfect numbers## 121

Find a number base other than 10 in which 121 is a perfect square.

## Adding bases

Let \(a_b\) denote \(a\) in base \(b\).

Find bases \(A\), \(B\) and \(C\) less than 10 such that \(12_A+34_B=56_C\).

## Reverse bases again

Find three digits \(a\), \(b\) and \(c\) such that \(abc\) in base 10 is equal to \(cba\) in base 9?

## 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.