mscroggs.co.uk
mscroggs.co.uk

subscribe

# Puzzles

## Archive

Show me a Random Puzzle
▼ show ▼

## 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?

## One Hundred Factorial

How many zeros does $$100!$$ end with?
© Matthew Scroggs 2018