# 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

probabilty multiples rectangles games ellipses grids chocolate rugby probability integers geometry sums factors spheres time wordplay perfect numbers symmetry integration regular shapes trigonometry multiplication proportion people maths remainders square numbers money speed advent doubling sequences perimeter algebra ave 3d shapes unit fractions percentages chess cards planes surds dates calculus complex numbers shapes division addition coins floors balancing prime numbers partitions books functions polygons taxicab geometry triangle numbers folding tube maps 2d shapes angles graphs means dodecagons bases chalkdust crossnumber clocks square roots colouring pascal's triangle indices fractions triangles logic cryptic crossnumbers irreducible numbers shape dice area arrows scales crosswords odd numbers differentiation factorials averages crossnumbers cube numbers hexagons lines numbers routes number menace parabolas sport volume squares cryptic clues digits palindromes quadratics sum to infinity star numbers mean coordinates circles christmas## Not Roman numerals

The letters \(I\), \(V\) and \(X\) each represent a different digit from 1 to 9. If

$$VI\times X=VVV,$$
what are \(I\), \(V\) and \(X\)?

## 20 December

Today's number is the sum of all the numbers less than 40 that are not factors of 40.

## 15 December

Today's number is smallest three digit palindrome whose digits are all non-zero, and that is not divisible by any of its digits.

## 13 December

There is a row of 1000 lockers numbered from 1 to 1000. Locker 1 is closed and locked and the rest are open.

A queue of people each do the following (until all the lockers are closed):

- Close and lock the lowest numbered locker with an open door.
- Walk along the rest of the queue of lockers and change the state (open them if they're closed and close them if they're open) of all the lockers that are multiples of the locker they locked.

Today's number is the number of lockers that are locked at the end of the process.

Note: closed and locked are different states.

## 7 December

There is a row of 1000 closed lockers numbered from 1 to 1000 (inclusive). Near the lockers, there is a bucket containing the numbers 1 to 1000 (inclusive) written on scraps of paper.

1000 people then each do the following:

- Pick a number from the bucket (and don't put it back).
- Walk along the row of lockers and change the state (open them if they're closed and close them if they're open) of all the lockers that are multiples of the number they picked (including the number they picked).

Today's number is the number of lockers that will be closed at the end of this process.

## 6 December

This puzzle is inspired by a puzzle that Daniel Griller showed me.

Write down the numbers from 12 to 22 (including 12 and 22). Under each number, write down its largest odd factor*.

Today's number is the sum of all these odd factors.

* If a number is odd, then its largest odd factor is the number itself.

## Digitless factor

Ted thinks of a three-digit number. He removes one of its digits to make a two-digit number.

Ted notices that his three-digit number is exactly 37 times his two-digit number. What was Ted's three-digit number?

## 24 December

Today's number is the smallest number with exactly 28 factors (including 1 and the number itself as factors).