# Puzzles

## Archive

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#### 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

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