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

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

Archive

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