mscroggs.co.uk
mscroggs.co.uk

subscribe

Sunday Afternoon Maths X

 Posted on 2014-04-27 

Lights

Source: Maths Jam
You have been taken captive and are blindfolded. There is a table in front of you with four lights on it. Some are on, some are off: you don't know how many and which ones. You need to get either all the lights on or all the lights off to be released. To do this, you can ask your captor to toggle the light switches of some of the lights. You captor will then rotate the table (so you don't know where the lights you toggled now are). Find a sequence of moves which will always lead to your release.

Show answer & extension

Princess problem

Source: Maths Jam
A princess lives in a row of 17 rooms. Each day she moves to a room adjacent to the one she wakes up in (eg. If she sleeps in room 5 today, then she will sleep in room 4 or 6 tomorrow). If you are able to find the princess by only opening one door each night then you will become her prince. Can you find her in a finite number of moves?

Show answer & extension

Three digit numbers

Brigette wrote down a list of all 3-digit numbers. For each of the numbers on her list she found the product of the digits. She then added up all of these products. Which of the following is equal to her total?
A \(45\)
B \(45^2\)
C \(45^3\)
D \(2^{45}\)
E \(3^{45}\)

Show answer & extension

Tags: numbers
If you enjoyed these puzzles, check out Advent calendar 2024,
puzzles about multiplication, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025