# Puzzles

## Archive

Show me a Random Puzzle**Most Recent Collections**

#### Sunday Afternoon Maths LIX

Turning SquaresElastic Numbers

Square Pairs

#### Sunday Afternoon Maths LVIII

Factorial PatternPlacing Plates

#### Advent Calendar 2016

#### Sunday Afternoon Maths LVII

Largest Odd FactorsList of All Puzzles

## 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 rectangles clocks menace routes taxicab geometry remainders chalkdust crossnumber palindromes sequences means unit fractions division square roots surds doubling quadratics indices symmetry planes volume number partitions ave pascal's triangle mean advent arrows## 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?

## Square Pairs

Source: Maths Jam

Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?

For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

## Factorial Pattern

$$1\times1!=2!-1$$ $$1\times1!+2\times2!=3!-1$$ $$1\times1!+2\times2!+3\times3!=4!-1$$Does this pattern continue?

## 24 December

Today's number is 191 more than one of the other answers and
100 less than another of the answers.

## 23 December

Today's number is the number of three digit numbers that are not three more than a multiple of 7.

## 22 December

Today's number is a palindrome. Today's number is also the number of palindromes between 111 and 11111 (including 111 and 11111).

## 19 December

The sum of all the numbers in the eighth row of Pascal's triangle.

Clarification: I am starting the counting of rows from 1, not 0. So (1) is the 1st row, (1 1) is the 2nd row, (1 2 1) is the 3rd row, etc.

## 18 December

The smallest number whose sum of digits is 25.