More Fallible Friends

While I search for a copy of an old puzzle, I’ll post a new one of the same type:

So I asked five friends about a number they had seen, and each one told me two things about the number. Unfortunately, my friends are infallibly inconsistent – if they say two things, one is guaranteed to be right, one is guaranteed to be wrong, and it’s hard to tell which is which. Can you help find the secret number?

Abigail: It is a multiple of 3. And it is a prime.

Bernard: It has a 2 in it. And it is the product of two distinct primes.

Cassandra: It is a three-digit number. And it is even.

Declan: It does not have a 0 in it. And it does not have a 6 in it.

Ernestine: It is the product of three distinct primes. And it is a two digit number.

Have they told you enough? Do you know the number?

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I am producing more of these because one class is eating them up. There’s some number sense. There’s some reasoning. And at 5 minutes, and in exchange for enthusiasm the rest of the period, it’s an easy choice.

Notice that Declan is a more directly useful than some of the others. His statements can be combined into “has a 0 or a 6 but not both.”  If I were working with younger kids, I would use more of those sorts of pairs, for example “It is even and it is a multiple of 6” which narrows things quickly or “It is two digits and it is less than 50” which places an even tighter restriction.

Next most directly useful might be the combination of Cassandra and Ernestine. Notice how there are not 4 T/F choices, but only 2.

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I’m interested in feedback from anyone who has tried these (and enjoyed or not enjoyed them) or even more so, from anyone who has tried these with kids.