mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

Square factorials

Source: Woody at Maths Jam
Multiply together the first 100 factorials:
$$1!\times2!\times3!\times...\times100!$$
Find a number, \(n\), such that dividing this product by \(n!\) produces a square number.

Show answer & extension

Lots of ones

Is any of the numbers 11, 111, 1111, 11111, ... a square number?

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

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

Archive

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