[Brandonb]

Billy is racing in the Olympic 400m dash and is in last place (8th). Billy overtakes everyone in the race, except for the guy in third place. What place is Billy in now? why?

[Brandonb]

OK, maybe

starting positions. In a race everyone is staggered at the start, so the guy in 3rd is starting at the inner-most lane and Billy is starting to his right.

I don't quite follow.

Where would the 1st and 2nd place guys be? And if Billy was to the right of the 3rd place guy, wouldn't that make him 4th, not last?

[itachi-san]

I don't quite follow.

Where would the 1st and 2nd place guys be? And if Billy was to the right of the 3rd place guy, wouldn't that make him 4th, not last?

Well, this is obviously not the answer I suppose, but in a race it is not possible for some to be in 3rd place the whole time because of the staggered starting positions. Everyone starts in a different lane and then they all mesh after a few seconds and all stay on the inside lane, unless passing. So if the guy in 3rd starts at the innermost lane and Billy is on the second lane, then everyone passes Billy and takes their spots and Billy was never in front of the guy in 3rd.

[Brandonb]

Well, this is obviously not the answer I suppose, but in a race it is not possible for some to be in 3rd place the whole time because of the staggered starting positions. Everyone starts in a different lane and then they all mesh after a few seconds and all stay on the inside lane, unless passing. So if the guy in 3rd starts at the innermost lane and Billy is on the second lane, then everyone passes Billy and takes their spots and Billy was never in front of the guy in 3rd.

Ah, I see what you mean.

But that would mean that everyone had overtaken Billy. Not that Billy had overtaken everyone.

Also, that means the guy in 3rd would then be in 7th

[Guest]

He is in third because he overtook everyone except the people in first and second(that's where I fail) and is exactly tied with the person that has been in third the whole time.

Edited April 11, 2008 by DemonWolf44

[Brandonb]

He is in third because he overtook everyone except the people in first and second(that's where I fail) and is exactly tied with the person that has been in third the whole time.

Earlier post....

The man in 3rd place clearly remains in third place, no ties or simultaneous transitions.

Work along the lines of "what makes this statement impossible? So then what makes it possible?"

The answer is very much inside the box. You may kick yourself when the answer is revealed.

[Guest]

Perhaps he was two laps behind, and he passed them all (still don't see how he didn't overtake third place guy, but this is all i can think of), and thus was still in 8th place.

[Guest]

Perhaps he was two laps behind, and he passed them all (still don't see how he didn't overtake third place guy, but this is all i can think of), and thus was still in 8th place.

400 meters is one lap.

[bonanova]

Billy is racing in the Olympic 400m dash and is in last place (8th). Billy overtakes everyone in the race, except for the guy in third place. What place is Billy in now? why?

Eighth - because the OP says he's in 8th.

But I have to note that your OP has a lot of things happening in the present.

[1] Billy is in 8th place. present tense.

[2] Billy overtakes everyone except the 3rd place guy. present tense.

[3] What place is Billy in now? Present tense.

But if he overtakes everyone except for one person, then he's in 2nd

[Brandonb]

Eighth.

I see what you mean, my context is a little off.

But in the answer that I'm looking for he can't be in eighth, maybe I should have clarified that he was in last place (8th), then he overtakes everyone...

[bonanova]

Say "the guy in 3rd place" is named John.

So at some point, Billy was in 8th place and John was in 3rd place.

... then ...

Billy overtook everybody but John.

Of the eight runners, there are now six runners behind Billy [not himself, and not John], so

... now ...

Billy is in 2nd place [trailing only John].

I'm thinking, for some reason, that this is not the answer you're looking for.

I'm curious to hear what it is ...

[Brandonb]

Say "the guy in 3rd place" is named John.

So at some point, Billy was in 8th place and John was in 3rd place.

... then ...

Billy overtook everybody but John.

Of the eight runners, there are now six runners behind Billy [not himself, and not John]

... now ...

Billy is in 2nd place [trailing only John].

Not quite...

That's the rub... Billy never passes the guy in 3rd place. The guy in third place is in third place, he is not first or second or anything else.

[bonanova]

Not quite...

That's the rub... Billy never passes the guy in 3rd place. The guy in third place is in third place, he is not first or second or anything else.

We agree he did not pass John.

That's why he's not in first place.

The OP says he passed everyone except John.

That's why he is in 2nd place. He passed everyone else.

The OP is ambiguous with everything in present tense.

Remove present tense and take things in sequence and you get this.

And you underlined "everyone in the race except ...." that has to include the ones who were then in 1st and 2nd place.

Anyway, I get what you're saying.

[onetruth]

Maybe he is the guy in 3rd place, and at some point he overtook all the other runners, but fell behind again.

[Brandonb]

We agree he did not pass John.

That's why he's not in first place.

The OP says he passed everyone except John.

That's why he is in 2nd place. He passed everyone else.

You made the OP ambiguous by putting everything into present tense.

Remove present tense and take things in sequence and you get this.

And you underlined "everyone in the race except ...." that has to include the ones who were then in 1st and 2nd place.

haha, but does it???

think again. Logic... if, then...

[Brandonb]

OK the answer for what position he is in is....

4th place

Keep trying to figure out why/how

I'll post that answer tomorrow!

[Guest]

OK the answer for what position he is in is....

4th place

Keep trying to figure out why/how

I'll post that answer tomorrow!

Huh. 5 pages and 12 hours ago Toddpeak stated it pretty clearly and I never understood your refutation, certainly not given the bounds of your OP. Obviously Billy changed position (from 8th to 4th) and it's safe to assume that others would as well. Since the problem is stated in present tense, we assume that the race is still in progress. When you say he has not overtaken "the guy in third place," we would rightly conclude that the "guy in third place" is in that position at the present moment, but why should we conclude that he was always in that position?

In fact, the runner in 3rd place could not have been there the whole time without simultaneous transitions, which you've already dismissed, since A) we know Billy passed the runners currently at 1st and 2nd, B) they couldn't have been in those positions at the time he passed them, so C) they must have passed the runner currently in 3rd at a later time, and in doing so, the position of the runner currently at 3rd would have changed.

I suspect this is a case of fishing for a specific response without realizing that there are other responses that meet the criteria of the question just as well. In any case, what about ...

At the moment in time that the problem is stated we have:

1st: John

2nd: Lancelot

3rd: Bob

4th: Billy

Earlier in the race we had the following two events:

1. Billy passes John and Lancelot. (Bob is in front of all three)

2. John and Lancelot pass Billy and Bob.

This is essentially the same as what Toddpeak suggested, with the only difference being that I didn't assume that Billy made it up to 2nd place at any time. And based on the criteria you provided, Todd's statement that he could be in any position greater than 4 makes perfect sense as well. I'm curious how your answer will differ.

[Guest]

4th place.Billy was in last place,before to start the race

Billy is racing in the Olympic 400m dash and is in last place (8th). Billy overtakes everyone in the race, except for the guy in third place. What place is Billy in now? why?

Edited April 12, 2008 by ash013

[bonanova]

OK the answer for what position he is in is....

I'll post that answer tomorrow!

4th place

Keep trying to figure out why/how

How could three runners still be in front of him?

It's not difficult to see that if the runner who finishes the race in 3rd place - call him Jack - is in front of Billy, then Billy finishes in 4th place.

But that is not consistent with the OP, which implies Billy passed six runners: every runner except the guy [singular] in 3rd place.

Net:

[1] Either the rules of the OP say 8 and 3 can't change -- then Jack is still in 3rd place and Billy is still in 8th place.

[2] Or the rules permit 8 and 3 to change -- then Jack is now in 1st place and Billy is now in 2nd place.

You could argue that we're not talking about particular runners [Jack]; we're just saying what places [just the 3rd place guy] weren't passed.

That is, Billy doesn't pass everyone except Jack, he passes the runners who are in all the positions except for 3rd position.

Billy passes

the 7th place runner

the 6th place runner

the 5th place runner

the 4th place runner

the 2nd place runner and

the 1st place runner.

As a result, there are three runners in front of him.

Winning that argument will get a tip of the cap.

[itachi-san]

OK, it's gotta be 1 of 2 things:

1)You're logic is flawed

2)You stumped us all (well at least me, I'm completely baffled as to how this can work)

Edit: Given that:

1)3rd place ever changing

2)simultaneous overtakings

3)Every position Billy can be in except 4th

Edited April 12, 2008 by itachi-san

[Brandonb]

Huh. 5 pages and 12 hours ago Toddpeak stated it pretty clearly and I never understood your refutation, certainly not given the bounds of your OP. Obviously Billy changed position (from 8th to 4th) and it's safe to assume that others would as well. Since the problem is stated in present tense, we assume that the race is still in progress. When you say he has not overtaken "the guy in third place," we would rightly conclude that the "guy in third place" is in that position at the present moment, but why should we conclude that he was always in that position?

In fact, the runner in 3rd place could not have been there the whole time without simultaneous transitions, which you've already dismissed, since A) we know Billy passed the runners currently at 1st and 2nd, B) they couldn't have been in those positions at the time he passed them, so C) they must have passed the runner currently in 3rd at a later time, and in doing so, the position of the runner currently at 3rd would have changed.

I suspect this is a case of fishing for a specific response without realizing that there are other responses that meet the criteria of the question just as well. In any case, what about ...

At the moment in time that the problem is stated we have:

1st: John

2nd: Lancelot

3rd: Bob

4th: Billy

Earlier in the race we had the following two events:

1. Billy passes John and Lancelot. (Bob is in front of all three)

2. John and Lancelot pass Billy and Bob.

This is essentially the same as what Toddpeak suggested, with the only difference being that I didn't assume that Billy made it up to 2nd place at any time. And based on the criteria you provided, Todd's statement that he could be in any position greater than 4 makes perfect sense as well. I'm curious how your answer will differ.

Wrong, just wrong. You are assuming that there is something wrong in the OP, there is not.

The only thing anywhere close is that I have an order of events presented in the present tense.

You are still assuming things that are logically impossible.

[Brandonb]

How could three runners still be in front of him?

It's not difficult to see that if the runner who finishes the race in 3rd place - call him Jack - is in front of Billy, then Billy finishes in 4th place.

But that is not consistent with the OP, which implies Billy passed six runners: every runner except the guy [singular] in 3rd place.

Net:

[1] Either the rules of the OP say 8 and 3 can't change -- then Jack is still in 3rd place and Billy is still in 8th place.

[2] Or the rules permit 8 and 3 to change -- then Jack is now in 1st place and Billy is now in 2nd place.

You could argue that we're not talking about particular runners [Jack]; we're just saying what places [just the 3rd place guy] weren't passed.

That is, Billy doesn't pass everyone except Jack, he passes the runners who are in all the positions except for 3rd position.

Billy passes

the 7th place runner

the 6th place runner

the 5th place runner

the 4th place runner

the 2nd place runner and

the 1st place runner.

As a result, there are three runners in front of him.

Winning that argument will get a tip of the cap.

Take the OP as the order in which the events occurred. In this argument that you present, the 3rd place is now in 1st. Billy never makes it past 4th place. Keep trying.

[Brandonb]

FINE, I guess it is technically tomorrow where I am, so I will give you the answer.

OP- Billy is racing in the Olympic 400m dash and is in last place (8th). Billy overtakes everyone in the race, except for the guy in third place. What place is Billy in now? why?

IF Billy overtakes everyone in the race, except for the guy in 3rd (who is always in third), THEN the guys in 1st and 2nd cannot be in the race.

So this means either...

A- 1st and 2nd didn't start the race (doesn't work for obvious reasons)

B- 1st and 2nd dropped out of the race (which is does not satisfy the OP because then 3rd would be first)

OR

C- 1st and 2nd have finished the race already, so they are not in the race. (and the places remain the same)

Because 1st and 2nd have finished the race (they are not in the race), and Billy overtook everyone in the race except for the guy in 3rd, then Billy is in 4th. (ie. he overtakes the guys in positions 7,6,5,4 but cannot overtake position 3)

I hope this is clear

The logic is solid. It's the 1 solution that fits the OP.

Edited April 12, 2008 by Brandonb

[itachi-san]

FINE, I guess it is technically tomorrow where I am, so I will give you the answer.

OP- Billy is racing in the Olympic 400m dash and is in last place (8th). Billy overtakes everyone in the race, except for the guy in third place. What place is Billy in now? why?

IF Billy overtakes everyone in the race, except for the guy in 3rd (who is always in third), THEN the guys in 1st and 2nd cannot be in the race.

So this means either...

A- 1st and 2nd didn't start the race (doesn't work for obvious reasons)

B- 1st and 2nd dropped out of the race (which is does not satisfy the OP because then 3rd would be first)

OR

C- 1st and 2nd have finished the race already, so they are not in the race. (and the places remain the same)

Because 1st and 2nd have finished the race (they are not in the race), and Billy overtook everyone in the race except for the guy in 3rd, then Billy is in 4th. (ie. he overtakes the guys in positions 7,6,5,4 but cannot overtake position 3)

I hope this is clear

The logic is solid. It's the 1 solution that fits the OP.

What you are saying is clear, it's just very flawed... If 1st and 2nd finished the race then they are in the race, they are just not running at the time. By your logic you have to say he doesn't overtake 1st, 2nd or 3rd because all 3 of those positions will finish before he does. There is no reason to single out the 3rd place runner.

[Guest]

What you are saying is clear, it's just very flawed... If 1st and 2nd finished the race then they are in the race, they are just not running at the time. By your logic you have to say he doesn't overtake 1st, 2nd or 3rd because all 3 of those positions will finish before he does. There is no reason to single out the 3rd place runner.

I'd agree with itachi-san, especially because of the issues with tense in the OP. If someone finishes a race 1st or 2nd then I would say that they were definitely "in the race".

I would also argue that a race is not over until the last person finishes, otherwise if every time someone crossed the finish line they were removed from the race then that would mean everyone would finish in 1st place. E.g. when all but the last person have finished, if they are no longer in the race then it is a race of 1 person, so the last person must finish 1st, which obviously isn't right (and also makes your answer of 4th incorrect).

Edited April 12, 2008 by neida

[Brandonb]

What you are saying is clear, it's just very flawed... If 1st and 2nd finished the race then they are in the race, they are just not running at the time. By your logic you have to say he doesn't overtake 1st, 2nd or 3rd because all 3 of those positions will finish before he does. There is no reason to single out the 3rd place runner.

If first and second finished, they are in the race? Tell me how? A race does not consist of someone finishing, then racing on in hopes of.... nothing. They are no longer in the race, they can lay down on the ground if they want to. They are no longer competing, they are no longer in the race. It's plain, simple and accurate.

Sure, they would have been in the race to start. But by my logic, I had to say that he overtakes everyone in the race except 3rd. At the point that Billy passed everyone, the only person still in front of him that was in the race and he could not pass was the 3rd runner. It is impossible for this to play out any other way, it is the only option from the information given.

There IS a reason to single out the 3rd place runner. -That is what makes the riddle... you concentrate so hard on how he passes 1st and 2nd, when it is actually just plain impossible.

*You are watching a race, the guy in last place catches up to 4th place and the 1st and 2nd place guys have finished*

That is the scenario of OP, straight forward. Like I said, Inside the box.