Puzzle

[Bigmallly]

Sorry William but I don't think you are doing your niece any favours by posting questions for her on the vine...........only my opinion.

[WilliamD]

She'd worked out the answers to the other questions, got stuck on this one and asked her Mum and Dad, neither of whom could get it. They asked me and I couldn't either. Thanks to Martin, a bunch of us adults as well as one youngster have learned a valuable and interesting technique of deduction. I'd far rather that than being left mystified.

[Bigmallly]

I appreciate you being intrigued about how the answer was arrived at but if it's part of her half term homework it may have been better to wait until they returned the work.

[Alison]

Rosti know the hour. He can only be sure that Ann doesn't know unless all the minute numbers on his hour are not unique.

What about the situation where two numbers are not unique and one is? This is true of 6. If Ann knew the minutes was 32 the hour could still be 6 or 8 and likewise there would be two non unique options for 19 and 50 mins. Either way surely she still won't know between the two non unique numbers. It can't be 43 or 46 as they're totally unique and that only leaves 7.17 on the seventh hour so it can't be that either. Have I misunderstood your reasoning?

[Bigmallly]

Well for what it's worth, I don't think Lonnie leaves the house till 0920.

[Martin H]

What about the situation where two numbers are not unique and one is? This is true of 6. If Ann knew the minutes was 32 the hour could still be 6 or 8 and likewise there would be two non unique options for 19 and 50 mins. Either way surely she still won't know between the two non unique numbers. It can't be 43 or 46 as they're totally unique and that only leaves 7.17 on the seventh hour so it can't be that either. Have I misunderstood your reasoning?

Alison, you have to look first from Rosti's perspective...

Suppose Lonnie's train actually left at 6:32. Then Rosti, who knows it was 6:something, would NOT be able to say that Alison didn't know the answer. From his perspective the train might leave at 6:43 in which case she would know, because there is only one 43 on the timetable.

Therefore the hour can't be 6. Or indeed 7, using the same logic.

[veggiechicken]

I'm still confused!
If Rosti knows it 8, he wouldn't know whether it was 8.19 or 8.32 as neither of these minutes are unique
If Ann knew it was 32, why would she suddenly decide it was 8.32, not 6.32?........

[Martin H]

We might need a mod to close this thread soon...

I'm still confused!
If Rosti knows it 8, he wouldn't know whether it was 8.19 or 8.32 as neither of these minutes are unique

Correct... until Ann replies, ‘I didn’t know his train, but now I do.’

If Ann knew it was 32, why would she suddenly decide it was 8.32, not 6.32?........

Because Rosti said that he knows Ann doesn't know. Ann can then work out it can't be 6:anything or 7:anything, as per the reasoning in my last post.

This is a very good puzzle: every statement in the puzzle is necessary to find the solution, there is nothing redundant at all.

[Alison]

Alison, you have to look first from Rosti's perspective...

Suppose Lonnie's train actually left at 6:32. Then Rosti, who knows it was 6:something, would NOT be able to say that Alison didn't know the answer. From his perspective the train might leave at 6:43 in which case she would know, because there is only one 43 on the timetable.

Therefore the hour can't be 6. Or indeed 7, using the same logic.

Although there is only one 43 on the timetable (agreed it can't be that specific time) there are still two other 6 times ie 6.32 and 6.50 so Rosti wouldn't know which of those it was (if he knew it was 6) and both 32 and 50 are used elsewhere (6.32 and 8.32) (6.50 and 9.50) so I don't see how you say it can't be 6. The same goes for 8 and 9.

[Guest]

Actually.......Lonnie doesn't get a train cos Rosti is something you eat and Ann is going round for dinner

Its ok I am going

[Martin H]

Although there is only one 43 on the timetable (agreed it can't be that specific time) there are still two other 6 times ie 6.32 and 6.50 so Rosti wouldn't know which of those it was (if he knew it was 6) and both 32 and 50 are used elsewhere (6.32 and 8.32) (6.50 and 9.50) so I don't see how you say it can't be 6.

One step at a time, Alison... it's necessary to take the puzzle statements in the order given and follow a process of elimination.

Rosti's first statement was ‘I don’t know when Lonnie’s train leaves, but I’m sure that neither does Ann.’

The important piece of information here is, "I'm sure that neither does Ann".

If the hour was 6, Rosti could not have this certainty, because on the information he has at this point, the minutes might be 43. Therefore the hour cannot be 6.

While I'm here, let's finish the solution.

The same logic rules out the hour being 7: Rosti cannot be certain that Ann doesn't know the exact time because if the minutes were 46 she would indeed know the exact time. Therefore the hour cannot be 7 either. The only remaining possibilities are that the hour is 8 or 9.

Once that's settled, we can move onto the next statement, where Ann says, ‘I didn’t know his train, but now I do.’

What changed for Ann to be able to say this? It's the knowledge that Rosti knew she didn't know the answer. This knowledge allows Ann to work out that the hour must be 8 or 9, using the exact same logic spelled out above. This must be enough for Ann to know the exact time, so we can deduce that the minutes cannot be 19 because both 8:19 and 9:19 are on the timetable. In fact the only remaining possibilities are now 8:32, 9:17 and 9:50.

We're nearly there...

Finally, Rosti responds, ‘Now I do as well!’

This eliminates the possibility of the hour being 9, because there would have been two live possibilities and Rosti wouldn't be know which it was. The only possibility left is 8:32.

[Alison]

One step at a time, Alison... it's necessary to take the puzzle statements in the order given and follow a process of elimination.

Rosti's first statement was ‘I don’t know when Lonnie’s train leaves, but I’m sure that neither does Ann.’

The important piece of information here is, "I'm sure that neither does Ann".

If the hour was 6, Rosti could not have this certainty, because on the information he has at this point, the minutes might be 43. Therefore the hour cannot be 6.

While I'm here, let's finish the solution.

The same logic rules out the hour being 7: Rosti cannot be certain that Ann doesn't know the exact time because if the minutes were 46 she would indeed know the exact time. Therefore the hour cannot be 7 either. The only remaining possibilities are that the hour is 8 or 9.

Once that's settled, we can move onto the next statement, where Ann says, ‘I didn’t know his train, but now I do.’

What changed for Ann to be able to say this? It's the knowledge that Rosti knew she didn't know the answer. This knowledge allows Ann to work out that the hour must be 8 or 9, using the exact same logic spelled out above. This must be enough for Ann to know the exact time, so we can deduce that the minutes cannot be 19 because both 8:19 and 9:19 are on the timetable. In fact the only remaining possibilities are now 8:32, 9:17 and 9:50.

We're nearly there...

Finally, Rosti responds, ‘Now I do as well!’

This eliminates the possibility of the hour being 9, because there would have been two live possibilities and Rosti wouldn't be know which it was. The only possibility left is 8:32.

Alternatively Ann wasn't really concentrating and despite having a unique number was busy eating biscuits. Rostie assumed she didn't know. She then finished the biscuit and looked properly so did then admit to knowing. Rosti then thought he knew but as neither of them told the other what they thought then they might have different solutions . Personally I'm of the belief that Lonnie was up to no good and didn't want them to know!

[lottie dolly]

I am more confused than ever,send the men in white coats,i will be waiting on the front