Let it go
Anne and Rashad each told me how many times they have seen the movie
Frozen
. I told them, “You have both seen
Frozen
, but one of you has seen it one more time than the other has.” Then I walked away, and they had this rather unusual conversation:
Anne: I don’t know how many times you’ve seen it.
Rashad: I don’t know how many times you’ve seen it either.
Anne: Oh, in that case I do know.
Rashad: Oh, then I do too.
How many times has Anne seen Frozen ?
Image credit: Disney
The answer is 2.
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1 solution
If either Anne or Rashad had seen Frozen only once, that person would know the other's count right off the bat (it would have to be 2).
Since learning this is not the case for Rashad makes all the difference to Anne, she must have thought it a possibility. The only way she could think that Rashad's count might have been 1 is if her count was 2.
Here's how it plays out:
What Anne knows: I've seen Frozen 2 times.
What Rashad knows: I've seen Frozen 3 times.
What Anne learns: He's seen it either 1 or 3 times.
What Rashad learns: She's seen it either 2 or 4 times.
What Rashad learns: that Anne's count is not 1 -- but he already knew this.
What Anne learns: Rashad's count can't be 1, so it must be 3.
What Rashad learns: Anne's count can't be 4, or she would have learned nothing from my last statement. It must be 2.
This is all just practice for learning how to think about the so-called Impossible Problem , which is a true gem (not composed by me).