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Grandpa's Rock Cakes

Weekly Problem 34 - 2012
Grandpa made a super-heavy rock cake. Five people have guessed the weight of the cake. Can you work out the weight of his cake?

How Would You Score It?

Stage: 3 Challenge Level: Challenge Level:1

Victor from St. Pauls School in Brazil, and Alice from the British School in Manila suggested similar arguments for each child:

Child number 1 would argue that they have the smallest correct range.

Child number 2 would argue that 88 is almost exactly in the middle of their range.

Child number 3 would argue that 88 was the first number in their range.

Child number 4 might say that the correct weight is just 2 away from the first number in their range.

Child number 5 could argue that he was the only one to enter a weight, not just guess a range of weights (so in an unfair way, he had the smallest chances of getting it right).

They would choose child 5 as he had by far the smallest chances and even so he almost got it right.


Huw from Cowbridge Comprehensive School in Wales devised this scoring system that penalised students who had chosen a wide range of values and rewarded students whose median value was close to Mr Jones' actual weight.

Ben and Joe, from the same school, and Daniel from King's School in New Zealand, suggested the same scoring system. Here is how Ben and Joe worked out who had done best:

Ben's solution

Joe's solution


Matthew from Moonee Ponds Central School in Australia suggested this scoring system:

Find the difference between the actual weight and both ends of the range.

Pick the larger number and subtract it from 100 to get your score.

The highest score wins. 


Thank you to Sophie from The King's Junior School in Chester and to the many students from Mount Pleasant Primary School who also offered their opinions.