Can you solve the private eye riddle? - Henri Picciotto
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For example, 41 (which is already prime), or 41075 → 41|07|5. Explore slime numbers in this worksheet (It is excerpted from the materials in Henri Picciotto’s Infinity, an elective high school math course).
When thinking about whole numbers, it is convenient to quickly recognize multiples of certain numbers. (For example, all multiples of 5 end in 0 or 5.) Wikipedia has a big list of divisibility tests.
Want more puzzles? TED-Ed has lots of fun and challenging brainteasers in our Riddle Series!

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