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


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


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


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