[Logic Puzzle] The Riddler's Challenge \ stacker news ~science

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764 sats \ 17 comments \ @SimpleStacker 27 Nov science

Batman, Robin, and Alfred wake up tied to chairs. They each have a number on their forehead. They can't see their own numbers, but they can see each others'.

The Riddler's voice pipes in from the intercom: "I've put a positive integer on each of your foreheads. Two of the numbers add up to the third. If any of you can guess your own number, you're all free to go. But if any of you guess wrong, Gotham City is blowing up!"

Batman starts by saying, "I don't know my number." Robin then says, "Neither do I." Then finally, Alfred, "Nor I." But after a few seconds, Batman says, "I now know my number!"

If Robin's number was 20 and Alfred's 30, what number did Batman have?

First stacker with the correct answer along with a complete explanation gets 1,000 sats!

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0 sats \ 8 replies \ @south_korea_ln 27 Nov

Can we assume all three integers are different?

Then

. If not, I don't see how to solve it.

0 sats \ 7 replies \ @SimpleStacker OP 27 Nov

You don't have to assume all three integers are different. There is a version of this problem where it is assumed all three integers are different, in which case @Fiat_Revelation's solution would be correct.

However, I don't think that requirement is necessary. There is another logical path that doesn't require the integers to be different. I hope that I'm correct in my assessment!

521 sats \ 6 replies \ @south_korea_ln 27 Nov

The plot thickens~~ I had the same reasoning as @Fiat_Revelation. I think I got it then. Following the same reasoning as outlined by @Fiat_Revelation (but cutting short on the different number assumption), we now need to argue on the relationships being used for each case, namely:

and

, then Alfred would have known his answer, because only equation (3) gives a valid combination of numbers for both Robin and Alfred. The other valid combination is obtained by Equation (2) and (1), respectively, for Robin and Alfred. However, he did not know the answer, in which case must

and that's what Batman says on his second round.

0 sats \ 0 replies \ @SimpleStacker OP 27 Nov

I'm still not sure if this logic works out. If it does then ultimately Batman can't be sure because Alfred knows his number if Batman is 10 also! Which would mean the problem is either bad or Alfred is not a trained logician

In either case, 500 sats for elucidating the hint :)

0 sats \ 4 replies \ @south_korea_ln 27 Nov

0 sats \ 1 reply \ @SimpleStacker OP 27 Nov

I'm not sure I followed your answer, but in the bottom right box shouldn't it be A -> 70? Not sure if that changes your logic.

Since it seems like few people will be attempting this further, I will give another hint.

Suppose the configuration is (10, 20, 30).

When it gets to Alfred, he knows he's either 10 or 30.

But if he's 10, what would Robin have seen during his first round?

0 sats \ 0 replies \ @south_korea_ln 27 Nov

Yes, 70, not 80. Doesn't change my logic though. I'll give it some more thought later using your hint, and see if it agrees or disagrees with my logic.

0 sats \ 1 reply \ @Fiat_Revelation 27 Nov

Lmao, I've been laying in bed trying to work this out in my head, but at this point I'm throwing in the towel.

0 sats \ 0 replies \ @SimpleStacker OP 27 Nov

It's a tough one!

0 sats \ 5 replies \ @Fiat_Revelation 27 Nov

I think it's 50.

Batman would know in theory 10 or 50 are possible, but has no way of being certain until the other two also declare that they don't know.

If it were 10, then Robin would look and see 10 and 30, meaning he also has no say of knowing his number (it could be 40 or 20). Alfred would look and see 10 and 20, meaning he would be able to guess his number correctly. Alfred would know the options for his number are 10 or 30 (since 10+10=20 and 10+20=30). He would know it can't be 10 because Riddler implied there were three integers. In this case, Alfred would know his is 30.

Since Batman trusts when Alfred says he doesnt know, he can therefore rule out 10 from being his own number. He then knows it's 50.

0 sats \ 4 replies \ @SimpleStacker OP 27 Nov

Oooh, this is very close, but it's not quite accurate of an explanation. Riddler didn't say that the three integers had to be unique.

1000 sats \ 3 replies \ @Fiat_Revelation 27 Nov

OK I'm back.

Alfred would have known his isn't 10, because if it were and so were batman's, then Robin would be able to deduce his is 20. This is because he sees 10 and 10. He knows 20-10=10 is not valid because Riddler wants only positive numbers. If Batman is 10, then Alfred knows his number. Batman is 50

33 sats \ 1 reply \ @SimpleStacker OP 27 Nov

Good job!

0 sats \ 0 replies \ @south_korea_ln 27 Nov

Ok, this makes sense.

0 sats \ 0 replies \ @Fiat_Revelation 27 Nov

I hope I didn't destroy Gotham

0 sats \ 0 replies \ @bief57 27 Nov

I have 2 theories

Batman can have the number 50 if we add the numbers of Robin (20) and Alfred (30)

2)Batman's number is 10, plus Robin's 20 gives Alfred's total of 30

0 sats \ 0 replies \ @south_korea_ln 27 Nov

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