# 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

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

## 22 December

In base 2, 1/24 is
0.0000101010101010101010101010...

In base 3, 1/24 is
0.0010101010101010101010101010...

In base 4, 1/24 is
0.0022222222222222222222222222...

In base 5, 1/24 is
0.0101010101010101010101010101...

In base 6, 1/24 is
0.013.

Therefore base 6 is the lowest base in which 1/24 has a finite number of digits.

Today's number is the smallest base in which 1/10890 has a finite number of digits.

Note: 1/24 always represents 1 divided by twenty-four (ie the 24 is written in decimal).

## 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.

## 9 December

Today's number is the number of numbers between 10 and 1,000 that contain no 0, 1, 2 or 3.

## 4 December

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

## Square and cube endings

Source: UKMT 2011 Senior Kangaroo

How many positive two-digit numbers are there whose square and cube both end in the same digit?

## 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?

## Backwards fours

Source: FiveThirtyEight

If A, B, C, D and E are all unique digits, what values would work with the following equation?

$$ABCCDE\times 4 = EDCCBA$$