mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

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

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

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

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

Archive

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