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westward comments on Brainstorming: children's stories - Less Wrong
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Not stories but...
Fermi estimates can be fun for kids (How many gumballs in this gumball machine is a classic) though for a three year old, it may be too advanced. How many action figures fit in this glass?
Three year olds can play "Guess the animal" which is 20 questions with some leeway on the yes/no part ("is it bigger or smaller than horse" is always our first question). Ingrain some binary search algorithms!