Riddle Me This

2 & 7

 

1 & 9?

 

i cant read chinese, thus i cannot solve this

 

0 and 9

 

one of the digits cannot be 0, because we need annie's clue in the denominator for dagmar's clue; and because of bert's clue, the numbers will need to be very minimal

it's probably 1, 2

 

I was thinking it was 1, 2... seems like Chester would have to think hard to figure it out.

 

Dagmar? Seriously? Not Doug? Dennis? Diane?

Dagmar?

 

1 & 3

 

why do you progress from Annie then to Bert?

why do you suggest that the clues given to students are linear?

... anything over 1 and 2 stop yielding unique sums

 

2 3 5 7
3 4 6 8
1 2 4 6

Spoiler

so, basically, one of the digits has to be one, and the other has to be 2 3 5 7. Dagmar won't know, because under all circumstances, he's gonna get the integer 2 (sucks to be him), so he's gonna cover all his bases with
[1,2]
[1,3]
[1,5]
[1,7]

annie, bert, and chester can find out their answers pretty easily.

 

wait...

 

From here, you can simplify quite a bit.

The only sums Bert could be certain about would be:

1 (0,1)
2 (0,2)
4 (1,3)
16 (7,9)
17 (8,9)

0 can't be involved, so that eliminates the first two.

4 & 16 would both yield a 2 from the subtraction, so that eliminates those two because the kid wouldn't be able to be certain there. That would leave 17 (8 & 9) as the only combo that would work.

I think.

 

Wow, I think this is right. Major props to you. Pun intended.

 

Bert cannot be certain about 2, as it can be 1+1. Neither about 4 (2+2 also possible) - 0 is also a non-negative number, and I don't see where it states explicitly that the numbers have to be different, so same numbers, e.g. 9,9 should also be possible.

Bert could be certain about 1 (0,1) or 17 (8,9) or 18 (9,9) only.

It cannot be 0,1 as Alice's clue would come out as 0 and you cannot divide by zero.

So it would have to be 8,9 or 9,9.

With 9,9, you would get

Alice = 9*9 = 81
Bert = 9+9 = 18
Chester = 9-9 = 0
Dagmar = 18/81 = 0.222222222

With 8,9, you would get

Alice = 8*9 = 72
Bert = 8+9 = 17
Chester = 9-8 = 1
Dagmar = (17+1)/72 = 0.25

I think both solutions would be correct, or am I missing something?? I mean, 0.25 sounds better as a solution, but how would 9,9 be wrong?

I guess I must be missing something, as only one solution can be correct...

I can only assume that the correct solution must be 8,9, and that the wording "non-negative number" is misleading, it should be "positive number", because only then you get only one possible solution.

 

Oh, didn't know it could be the same digit. Thought it had to be two different numbers.