mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

24 December

1,0,2,0,1,1
The sequence of six numbers above has two properties:
  1. Each number is either 0, 1 or 2.
  2. Each pair of consecutive numbers adds to (strictly) less than 3.
Today's number is the number of sequences of six numbers with these two properties
Tags: numbers

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

21 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10. Today's number is the smallest number you can make using the digits in the red boxes.
+÷= 2
× + -
×-= 31
+ + -
-×= 42
=
37
=
13
=
-2

Show answer

Tags: numbers, grids

20 December

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

17 December

For \(x\) and \(y\) between 1 and 9 (including 1 and 9), I write a number at the co-ordinate \((x,y)\): if \(x\lt y\), I write \(x\); if not, I write \(y\).
Today's number is the sum of the 81 numbers that I have written.

Show answer

Tags: numbers

16 December

Arrange the digits 1-9 in a 3×3 square so that the first row makes a triangle number, the second row's digits are all even, the third row's digits are all odd; the first column makes a square number, and the second column makes a cube number. The number in the third column is today's number.
triangle
all digits even
all digits odd
squarecubetoday's number

Show answer

Tags: numbers, grids

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

Archive

Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019