Perfect Information

Hello everyone

May someone tell me how to proceed to solve this kind of puzzle : https://brilliant.org/practice/perfect-information/?p=2 ?

"Alice and Bob are both given a different 1-digit number. Alice says, "I don't know your number, but I know mine is bigger than yours!" What is Alice's number?"

Please don t give me the solution, only how to preceed, thank you a lot.

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
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`\sum_{i=1}^3`	$\sum_{i=1}^3$
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`\boxed{123}`	$\boxed{123}$

Comments

If you think of it, Alice doesn't know Bob's number, but Alice is sure her number is bigger than his. Bob could have any number from 1 to 9, but still Alice is sure of it that her number is bigger, so, as you didn't ask the solution, just try to continue on this train of thought. This is a purely logical approach. If you use trial-and-error, it will work for this problem, as it is simple, but I do not suggest using it in the long run.

A Former Brilliant Member - 6 months, 2 weeks ago

Thank you for your response. However I have one more question ; for this kind of puzzles, may Us assume that Alice lie or are we sure she tells the truth ? Thank you ?

Ahmed Chikh - 6 months, 2 weeks ago

Well, in these kind of puzzles, you have to assume that they are both truthful and perfect logicians(perfect at logic). Only in question like Knights and Knaves, or Humans and Werewolves, where one part lies and other tells the truth, you have to use a different approach. Usually, it is given in the question what we must and mustn't assume.

A Former Brilliant Member - 6 months, 2 weeks ago

Thank you, I get it now !

Ahmed Chikh - 6 months, 2 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$