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Kate's Date
When Kate ate a giant date, the average weight of the dates decreased. What was the weight of the date that Kate ate?
Age 11 to 16
Challenge Level
Khue from British Vietnamese International School in Vietnam said:
An easier way of finding a mean weight for a combination of weights that is [the] numbers weights add up to a multiple of 5.
These diagrams illustrate Khue's reasoning:
or 
In fact, there are combinations of 3 kg and 8 kg weights which have means equal to 3, 4, 5, 6, 7 and 8 kg. Click to see them all.
mean = 3
mean = 4
mean = 5
mean = 6
mean = 7
mean = 8
Mahdi from Mahatma Gandhi International School in India used algebra to extend the problem to other pairs of weights:
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.