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Pumpkin Puzzle

On 6th November, Mr Dyer posed a puzzle about a pumpkin and asked for solutions from parents. Mr Dyer had a few responses, but no-one provided a justification for their answer … until now.

Luca Kopanyi in Year 7 sent a well set-out solution, demonstrating clarity of thought and excellent calculation. Her solution is below. Congratulations to Luca! 

If you wish to have another go yourself before reading Luca’s solution, the puzzle is this:

A huge Hallowe’en pumpkin weighed 100kg last week, and it was 99% water. It’s been left out in the garden for a week, and shrivelled up a bit. It’s now only 98% water. No animals have eaten any of the pumpkin. What does it weigh now?

Luca’s solution

Last week: Weight1 = 100kg

Percentages1                    

  • 99% water (W)
  • 1% something else (SE)

Weight1

  • 99kg W 
  • 1 kg SE
This week: Weight2 = ? kg

Percentages2                    

  • 98% water
  • 2% something else

Weight2

  • W = we don’t know
  • 1kg SE

So, last week the pumpkin weighed 100 kg and the pumpkin was 99% water and 1% something else and this week we don’t know how much the pumpkin weighs but we know that it is 98% water and 2% something else. We know that the something else bit stays the same and only the water percentage changes.

  • 1kg = 2% of weight2
  • 1kg = 0.02×weight2
  • So, 50kg = weight2

Weight of the pumpkin after 1 week = 50 kg

Richard Dyer

Principal