A case file has a few clues written on it, like "this number is even" or "this number is greater than 7." Cross off every suspect number that doesn't match a clue, and eventually just one culprit (the secret number) is left. This method of finding the answer by crossing off what doesn't fit the conditions is called "process of elimination."
Let's try an example. There are four suspects: 12, 15, 18, and 21. If the first clue is "this number is even," the odd numbers 15 and 21 are immediately crossed off, leaving only 12 and 18. If the second clue is "this number is a multiple of 3," neither one gets crossed off yet, since both are multiples of 3. Then the third clue, "this number is greater than 15," crosses off 12, leaving only 18. Every clue you add narrows the candidates down a little more.
The game features several kinds of clues. Basic clues tell you whether a number is even or odd, greater or less than some number, a multiple of some number, the sum of its digits, or its remainder when divided by something. The middle-school difficulty adds clues about whether a number is prime or a perfect square, making it a lot more challenging.
Process of elimination isn't just for this game. Solving a math problem often means narrowing in on the right answer by crossing off cases that can't possibly be it. Even looking for a lost object works the same way — "not in the kitchen, not in the living room" — narrowing down where it must be by ruling out where it isn't. Checking conditions one by one and narrowing down the candidates is a genuinely useful habit, not just in math but for solving all kinds of problems.
When playing with your child, have them say out loud, each time they check a clue, "can I cross this number off?" Solving it by pointing at or marking the numbers to cross off — rather than trying to do it all in their head — makes it much less confusing. Start on the easy difficulty to build a feel for it, and once they're comfortable, move up to the harder difficulty and try the new clues about primes and perfect squares.
On our activity page, a new case file is generated for each difficulty, and you check the clues to pick the culprit out from the suspects. Solve several cases and build a feel for combining clues to narrow down the candidates.