# 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## 11 December

Two more than today's number is the reverse of two times today's number.

## 4 December

Pick a three digit number whose digits are all different.

Sort the digits into ascending and descending order to form two new numbers. Find the difference between these numbers.

Repeat this process until the number stops changing. The final result is today's number.

## 1 December

Today's number is the smallest three digit number such that the sum of its digits is equal to the product of its digits.

## XYZ

Source: Futility Closet

Which digits \(X\), \(Y\) and \(Z\) fill this sum?

$$
\begin{array}{cccc}
&X&Z&Y\\
+&X&Y&Z\\
\hline
&Y&Z&X
\end{array}
$$## Elastic Numbers

*Throughout this puzzle, expressions like \(AB\) will represent the digits of a number, not \(A\) multiplied by \(B\).*

A two-digit number \(AB\) is called

*elastic*if:- \(A\) and \(B\) are both non-zero.
- The numbers \(A0B\), \(A00B\), \(A000B\), ... are all divisible by \(AB\).

There are three elastic numbers. Can you find them?

## 18 December

The smallest number whose sum of digits is 25.

## 10 December

The smallest number that is equal to the sum of its digits
multiplied by ten more than the sum of its digits.

## 6 December

When you add up the digits of a number, the result is called the digital sum.

How many different digital sums do the numbers from 1 to 10

^{91}have?** There was a mistake in this question (it previously said 10

^{92}). If you answered the typo'd question right, your answer should automatically correct itself to 9 less than it was...