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Ans: Quince, quonce, quance
7 quince weigh the same as 4 quance, so a quince weighs less than a quance. [1]
5 quance weigh the same as 6 quonce, so a quonce weighs less than a quance. [2]
So quance are the heaviest.
20 quance must weigh the same as 35 quince. (from [1])
20 quance must weigh the same as 24 quonce (from [2])
So 35 quince weigh the same as 24 quonce, so a quonce weighs more than a quince.
So quince is the lightest, and quance is the heaviest.
Three Fruits
Age 14 to 16
ShortChallenge Level 
Ans: Quince, quonce, quance
7 quince weigh the same as 4 quance, so a quince weighs less than a quance. [1]
5 quance weigh the same as 6 quonce, so a quonce weighs less than a quance. [2]
So quance are the heaviest.
20 quance must weigh the same as 35 quince. (from [1])
20 quance must weigh the same as 24 quonce (from [2])
So 35 quince weigh the same as 24 quonce, so a quonce weighs more than a quince.
So quince is the lightest, and quance is the heaviest.
This problem is taken from the UKMT Mathematical Challenges.
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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