Fallible Friends
Years ago on the Compuserve SciMat SIG, Bertie Taylor used to publish puzzles. One was “fallible friends” and I loved it. And as a teacher I made some of my own. This summer I taught in a math camp, and I made up some of my own Fallible Friends Puzzles.
These are logic puzzles. Look at each pair of statements about the secret number – one statement is true, one is false, but you don’t which is which. And it is your job to figure out what the secret number is.
Give these a try:
Cat and Dog
I ask two friends about a number. Each friend shares two facts – but each friend gets one “fact” right and one wrong.
Cat: The number is 1-digit.
Cat: The number is a perfect square.
Dog: The number is less than 50.
Dog: The number is less than 40.
Can you find the number?
Koala, Lemur and Meerkat
I have three fallible friends who get one thing right and one thing wrong. They see a number…
Koala says: “The number is odd. And it is a 2-digit number.”
Lemur says: “The number does not contain a 6. It does contain a 2.”
Meerkat says: “It is a power of 2. It is one more than a power of 3.”
What is the number?
Fox, Goat and Horse
[clumsy edit Fox/Goat/Horse permit multiple answers. So I’ve changed the question from “Help me figure out what the number is.” to “Help me figure out what the number might be (more than one possible answer.)”]
So I have 3 friends – each gets one thing right and one thing wrong. They see a number:
Fox : It is a 3-digit number
It is a multiple of 3.
Goat: It is a 1-digit number
It is 1 more than a 5th power
Horse: It is a multiple of 6.
It is a 2-digit number.
Help me figure out what the number might be (more than one possible answer.)
JD2718 
Hard to know how to comment on these without leaving spoilers :). The cat and the dog are cuddly and friendly and nice and lured me into believing these would be boring, but they’re not! I think the Koala, Lemur, and Meerkat allow two possible answers, one exactly 10 times the other. (My guess is that the larger of the two was the intended answer.)
This is fun! While Lemur/Meerkat MIGHT have more than one answer, I’m reasonably certain that one cannot be ten times the other… I think Meerkat’s clues guarantee something about Koala’s clues that make a factor of ten not possible.
I also think Fox, Goat, and Horse allow two possible answers, one that’s one digit and one that’s two digits?
Hmm… I think Fox and Goat allow more than one answer… but can’t see how a 2-digit number would work… Let’s play for the moment… I’ll revise them later.
Well you’re certainly right that I missed some!
I found the interaction between the Lemur and the Meerkat’s clues particularly charming.