mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

11 December

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

Show answer

4 December

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

Show answer

10 December

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

Show answer

Factorial pattern

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

Show answer

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.

Show answer & extension

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?

One hundred factorial

How many zeros does \(100!\) end with?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020