# 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

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

$$ABCCDE\times 4 = EDCCBA$$