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King's Maths School

Challenge 439: Who stole the cake?

Can you see through these lies and recover the delicious cake?

In each scenario, the following are true:

  • At least one alien is telling the truth, and at least one alien is lying
  • Exactly one alien stole the cake

In each scenario, who stole the cake? Make sure to include an explanation of your answer.

1) 

Arglbzz: "I stole the cake"

Brthflum: "Arglbzz stole the cake"

Clonk: "Brthflum didn't steal the cake"

2)

Arglbzz: "Brthflum stole the cake"

Brthflum: "It's my birthday today"

Clonk: "Anyone with an odd number of letters in their name is lying"

3)

Arglbzz: "The alien who stole the cake is lying"

Brthflum: "Exactly one of us is lying"

Clonk: "Exactly two of us are lying"

4)

Arglbzz: "Clonk didn't steal the cake"

Brthflum: "Arglbzz stole the cake"

Clonk: "This problem has a unique solution"

Submit your solution

Please do send in your solution to this problem to weeklymaths@kcl.ac.uk You can scan or photograph your written work, or type your solutions. If this is your first weekly maths challenge solution, please include your year group and the name of the school you attend. We'll be happy to provide feedback on your solution, assuming that you are in year 11 or below. If you are older than this, we hope you enjoy trying the problems and reviewing your solutions against those we publish on the website.