Math Problem - Page 2

If mike's number was D = 8, john would have M = 12. If john had M = 12, he would not know that mike didn't know it, because 12/2 is the only date with 2 as the day. John's first statement shows that he knows it is not a date that has only 1 date with the given day. This means his month cannot be 12 and it cannot be 6.

I would've understood it better if John just would've said: "Mike can't know the date". Because the if-clause is totally confusing and useless (John can't know the date in the first place with no information about Mike's number)

3/4

John says: "If I don't know the date, then Mike can't either"

(Mike, knowing he has 4 would deduce that it's either 3/4 or 6/4 at the beginning. John, having 3, knows it's 3/4, 3/5, or 3/8.)

Mike says: "I didn't know it at first, but now I know it"

if it was 6/4, John's statement would be false because John would have 6 which gives
the possibility of Mike knowing the answer right from the beginning

John says: "Now I know it too."

(John can use the same logic as Mike here to figure it out)

month
3-- | -- | -- | 4 | 5 | -- | 8
6-- | -- | -- | 4 | -- | 7 |-
9-- | 1 | -- | -- | 5 | -- |-
12 | 1 | 2 | -- | -- | -- | 8

then you clearly see which month have which days i common and you just have to cross out whole rows/colmns