Rimbo
1641
the older sibling beats up the younger siblings, leading to only one person to divide the money with, and takes it all
"relative speeds" as opposed to "relative position" makes Sirens answer(6), the first correct answer.
Rimbo
1643
Ahhhhhhhhhhhhhhhhhhhhhh… I see! You are quite correct.
Because if you know the relative speeds, once you run the sixth race – with any horse from each of the first six – you can calculate the relative speeds of all 25 against each other.
Ok, but let’s talk practicalities; how do you measure relative speeds without being able to measure exact speeds?
Doesn’t give you enough information. Let’s say you pick the third fastest horse in the first heat and race him against four new horses, and he places last. What information do you have to compare with for the two fastest horses in the first heat against the four in the second heat?
You can measure the distance the horse you use to measure against is behind or ahead when each horse crosses the finish line. If you know the length of the track and get accurate measurements of the distance between the horses you can get their relative speeds.
I feel like that presupposes a level of measuring that renders the inability to time horses meaningless. But I guess, yeah, you’re right.
Rimbo
1649
You could also have ratios. E.g., the first horse to finish gets a 1, second-place gets 1.02, third place is 1.05, fourth is 1.14, fifth is 1.23.
You do that for each race, then you treat those as coefficients. When you race one horse from each race against the others, you can calculate all of their speeds relative to each other. E.g. x1 is the first race multiplier, x2 is the second, etc. and y is the multiplier for the final race. So if you race the #1 horse from the first race in the sixth and he comes in third with a value of 1.07, then you know that x1=1.07. Thus the second-place horse from the first race is is 1.07x1.02, the third place is 1.05x1.07, etc.
If you were interviewing for a legal position, then finding and making the distinction between relative speed and relative position would be a great answer for the riddle. Otherwise, I think you’re splitting hairs on the wording. The key fact is that you have no stopwatch so you cannot compare times. So you can only compare relative performance using multiple runoffs.
If you want top poke all sorts of holes in the riddle, then one could point out that multiple runoffs with multiple horses over the same day does not effectively measure anything as other factors will confound your comparison. Some horse may recover from exertion quicker than others. This will allow them to perform better on a subsequent run versus on an earlier run. The time between runoffs will vary for the horse which again affect the amount of recovery. And depending on the runoff strategy used, some horse may have run more previous races than others.
Really, this riddle needs to be posed to QT3 using the standards from my pure math calculus classes which always posed problems start like this: “Suppose you have a perfectly uniform, and infinitely flat disc that was frictionless…”
Not having a stopwatch is the only restriction. Nothing says it needs to be in the same day. It’s not just for legal positions that the problem stating “relative speed” is important. Not having a stopwatch doesn’t mean you can’t have a camera.
[edit] - So, it does say “that day”. sorry. Still doesn’t mean anything, as the problem clearly states you CAN measure relative speeds. How you would do it is irrelevant.
Stop trying to solve the problem with a tape measure and use a sledgehammer! Run one heat, take the three fastest horses, and shoot the rest. Problem solved.
robsam
1653
That answer would get you hired at BP.
And it doesn’t mean you can’t have a metronome, so let’s use a metronome and count the ticks as a replacement for a stop watch. Problem solved!
Better yet, the riddle doesn’t say can’t have superimposed video recording like the one used in the 2010 Winter Olympics. We can film the five heats and just review the superimposed video!
This problem is absolutely trivial!
This is the reason I get annoyed at tournament systems, where the winners from each bracket place first and second. There’s a problem where the loser in a semifinal match might actually be better than the winner of the other bracket, and yet the semifinalist is stuck competing for third place. Ah, but I digress.
As for the horses, I like Siren’s answer (6) based on “relative speed” and not just on relative position, assuming that horse speed is consistent (a big caveat). The initial common-sense answer of “run 5 heats and then run the winners” actually works if, say, you have a photo of each finish. Just superimpose them all, using the 6th heat to calibrate. In fact, the horses in the 6th heat don’t even need to be the winners, just as long as they all come from different groups. Even better, you can rank-order all 25 horses that way.
That was an example of rationalization, it wasn’t a serious attempt to solve it. The important part is not that I’m adding stuff, it’s that other people are removing things from the problem in order to who the hell knows. If the problem says you know relative speed, you know relative speed. How is immaterial. It’s not “splitting hairs” to use the formulation of a problem to solve it, it’s what you’re supposed to do.
Erich
1657
1/2. The answer is always 1/2.
I have two children, one of whom is a son born on a Tuesday. What is the probability that I have two boys?
First thing you do is strip out the irrelevant information, being the “born on a Tuesday” qualifier. Knowing that you have one boy, the only options for your end state are BOY(known)-boy and BOY(known)-girl. Therefore, 1/2.
