mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

24 December

There are six 3-digit numbers with the property that the sum of their digits is equal to the product of their digits. Today's number is the largest of these numbers.

Show answer

22 December

In bases 3 to 9, the number 112 is: \(11011_3\), \(1300_4\), \(422_5\), \(304_6\), \(220_7\), \(160_8\), and \(134_9\). In bases 3, 4, 6, 8 and 9, these representations contain no digit 2.
There are two 3-digit numbers that contain no 2 in their representations in all the bases between 3 and 9 (inclusive). Today's number is the smaller of these two numbers.

Show answer

17 December

Eve picks a three digit number then reverses its digits to make a second number. The second number is larger than her original number.
Eve adds her two numbers together; the result is 584. What was Eve's original number?

Show answer

1 December

If you write out the numbers from 1 to 1000 (inclusive), how many times will you write the digit 1?

Show answer

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 \(X\)?

Show answer

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).

Show answer

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.

Show answer

9 December

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

Show answer

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

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

Archive

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