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Summer Maths Puzzles - Friday 2 August - Buckets of Fun

The parents decide that yesterday's activity was such fun that they're going to set the children another challenge today.   They tell the children that they'll take them sea kayaking once they've solved a bucket and spade (or rather just buckets) puzzle.

The children object strongly and say that they're far too old for buckets and spades!

Undaunted, and having spotted that each of the (rather large!) buckets has its capacity marked on the bottom, the parents set the children their next challenge.  The challenge is to make each whole number volume from 1 up to 12 using their three buckets which are of capacity 5 litres, 8 litres and 12 litres. 


To explain what they mean, they show the children how to make 7 litres using the buckets:

  1. Fill the 12 litre bucket
  2. Pour the water from the 12 litre bucket into the 5 litre bucket until the smaller bucket is full.
  3. The amount remaining in the 12 litre bucket is then the desired 7 litres.  

They show the children that this can be written down as follows:   0-0-12   5-0-7   0-0-7


Today's problem is to solve this latest challenge set by the parents, to figure out how to make all the whole number volumes from 1 up to 12 litres using the 3 buckets provided, so that the children get to go sea kayaking. 


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

  • Evgeny Mirkes
  • Andrea Chlebikova
  • Lindsay Woodhead
  • Nora Howie
  • Jennifer Evans
  • Kanha Seksaria
  • Fin Scott
  • Ali Raad
  • Soham Sud
  • Patrick Luo
  • Niall Moran
  • Emily and Jan
  • James Arthur
  • Alihan Huyuk
  • Isaac
  • Rosamund Riordan
  • Kalin Krishna
  • Georges Sbback
  • Austin family
  • Aaron Naidu
  • David Martí-Pete
  • Hana Dampf
  • Cong 
  • 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