A number leaves 2 when divided by 3, 3 when divided by 5, and 2 when divided by 7. The smallest it can be is 23 — and Sun Tzu asked exactly this in the third century.
The answer key prints on a separate page.
It is the rare question a nine-year-old can start and a first-year undergraduate can still find something in. Starting needs nothing but division with a remainder. Finishing well needs a method, and the method these sheets teach is a sieve rather than a formula: write the numbers that satisfy the first condition — they climb in steps of the first divisor — then check those against the second.
What makes the sieve worth teaching is what happens to the step. The numbers passing the first two conditions climb in steps of the two divisors multiplied, so the list to check against the third is short. Each condition multiplies the step, which is why the search finishes quickly and why a child can see that it must. The Chinese Remainder Theorem computes the same answer with a formula and shows none of that.