# Puzzles

## Archive

Show me a random puzzle**Most recent collections**

#### Sunday Afternoon Maths LXVII

Coloured weightsNot Roman numerals

#### Advent calendar 2018

#### Sunday Afternoon Maths LXVI

Cryptic crossnumber #2#### Sunday Afternoon Maths LXV

Cryptic crossnumber #1Breaking Chocolate

Square and cube endings

List of all puzzles

## Tags

partitions 2d shapes cryptic crossnumbers grids multiples polygons square roots addition integers remainders people maths means spheres percentages pascal's triangle sequences star numbers scales chocolate regular shapes shapes unit fractions colouring sums triangles rugby time taxicab geometry advent lines coordinates books bases menace crossnumbers sport angles games crosswords complex numbers chalkdust crossnumber perimeter parabolas folding tube maps palindromes numbers square numbers fractions doubling dodecagons wordplay clocks functions perfect numbers mean ave algebra prime numbers squares probabilty cube numbers 3d shapes symmetry sum to infinity indices rectangles multiplication planes probability factorials circles cryptic clues proportion coins christmas factors balancing shape area calculus volume hexagons irreducible numbers integration triangle numbers graphs digits logic number speed dates routes floors quadratics division arrows chess geometry averages trigonometry odd numbers surds dice money ellipses cards differentiation## 11 December

This puzzle is inspired by a puzzle Woody showed me at MathsJam.

Today's number is the number \(n\) such that $$\frac{216!\times215!\times214!\times...\times1!}{n!}$$ is a square number.

## 4 December

Today's number is the number of 0s that 611! (611×610×...×2×1) ends in.

## 10 December

How many zeros does 1000! (ie 1000 × 999 × 998 × ... × 1) end with?

## Factorial pattern

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

## Square factorials

Source: Woody at Maths Jam

Multiply together the first 100 factorials:

$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

## 17 December

In March, I posted the puzzle One Hundred Factorial, which asked how many zeros 100! ends with.

What is the smallest number, n, such that n! ends with 50 zeros?