skip to content

Summer Maths Puzzles - Thursday 1 August - 100 Pebbles

100 Pebbles

A family are on holiday.  The parents want to spend the morning lying peacefully on the beach.  The children want to go surfing.

The parents give the children a pack of 100 red stickers and tell them that before they can go surfing they should play a game with 100 rounds and the following rules:

  • In the first round they must collect 100 pebbles, place them in a straight line, and put a red sticker on each.
  • In the 2nd round they must turn over every 2nd pebble so that the sticker is no longer showing.
  • In the 3rd round they must turn over every 3rd pebble so that if the sticker was previously showing it no longer shows and vice versa.
  • In the 4th round they turn over every 4th pebble, in the 5th round they turn over the every 5th pebble and so on up to the end of the 100th round.

The parents say that they will take the children surfing when they tell them whether the 100th pebble has its sticker showing or not at the end of the game and how many times it was turned over during the game. 


The children go away and a few minutes later come back and tell their parents the correct answers.  What were their answers and how did they solve it?


Entry to this puzzle is now closed.  Congratulations to the following for some great answers: 

  • Junyang Wang
  • Andrea Chlebikova
  • Aaron Naidu
  • Jason Curran
  • Patrick Luo
  • Soham Sud
  • Emily Lies & Jan Ricken
  • Kanha Seksaria
  • Charlotte Harries-Harris
  • Jacob
  • Team Cabin
  • FiveTriangles
  • Fin Scott
  • Ian Slagle
  • Akshay Sant
  • Yulia and Christopher
  • Bethan
  • Phil Milner
  • Alex Austin
  • Alex Bell
  • Nora Howie 
  • Meg North
  • Ben Katz
  • Oree Golan

> Click here to return to the Summer Maths Puzzles homepage.


University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons