mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

2 December

Holly adds up the first six even numbers, then adds on half of the next even number. Her total is 49.
Next, Holly adds up the first \(n\) even numbers then adds on half of the next even number. This time, her total is 465124. What is \(n\)?

Show answer & extension

21 December

Arrange the digits 1–9 (using each digit exactly once) so that the three digit number in: the middle row is a prime number; the bottom row is a square number; the left column is a cube number; the middle column is an odd number; the right column is a multiple of 11. The 3-digit number in the first row is today's number.
today's number
prime
square
cubeoddmultiple of 11

Show answer

11 December

Today's number is the number \(n\) such that $$\frac{216!\times215!\times214!\times...\times1!}{n!}$$ is a square number.

Show answer

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?

Show answer & extension

16 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of rectangles (of any size) in a 2×19 grid of squares

14 December

There are 204 squares (of any size) in an 8×8 grid of squares. Today's number is the number of squares in a 13×13 grid of squares

What's the star?

In the Christmas tree below, the rectangle, baubles, and the star at the top each contain a number. The square baubles contain square numbers; the triangle baubles contain triangle numbers; and the cube bauble contains a cube number.
The numbers in the rectangles (and the star) are equal to the sum of the numbers below them. For example, if the following numbers are filled in:
then you can deduce the following:
What is the number in the star at the top of this tree?
You can download a printable pdf of this puzzle here.

Show answer

Square pairs

Source: Maths Jam
Can you order the integers 1 to 16 so that every pair of adjacent numbers adds to a square number?
For which other numbers \(n\) is it possible to order the integers 1 to \(n\) in such a way?

Show answer

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021

Advent calendar 2020


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2024