Riddle #822

logic

25 Horses

You have 25 horses. When they race, each horse runs at a different, constant pace. A horse will always run at the same pace no matter how many times it races. You want to figure out which are your 3 fastest horses. You are allowed to race at most 5 horses against each other at a time. You don't have a stopwatch so all you can learn from each race is which order the horses finish in. What is the least number of races you can conduct to figure out which 3 horses are fastest?
You need to conduct 7 races. First, separate the horses into 5 groups of 5 horses each, and race the horses in each of these groups. Let's call these groups A, B, C, D and E, and within each group let's label them in the order they finished. So for example, in group A, A1 finished 1st, A2 finished 2nd, A3 finished 3rd, and so on. We can rule out the bottom two finishers in each race (A4 and A5, B4 and B5, C4 and C5, D4 and D5, and E4 and E5), since we know of at least 3 horses that are faster than them (specifically, the horses that beat them in their respective races). This table shows our remaining horses: A1 B1 C1 D1 E1 A2 B2 C2 D2 E2 A3 B3 C3 D3 E3 For our 6th race, let's race the top finishers in each group: A1, B1, C1, D1 and E1. Let's assume that the order of finishers is: A1, B1, C1, D1, E1 (so A1 finished first, E1 finished last). We now know that horse D1 cannot be in the top 3, because it is slower than C1, B1 and A1 (it lost to them in the 6th race). Thus, D2 and D3 can also not be in the to 3 (since they are slower than D1). Similarly, E1, E2 and E3 cannot be in the top 3 because they are all slower than D1 (which we already know isn't in the top 3). Let's look at our updated table, having removed these horses that can't be in the top 3: A1 B1 C1 A2 B2 C2 A3 B3 C3 We can actually rule out a few more horses. C2 and C3 cannot be in the top 3 because they are both slower than C1 (and thus are also slower than B1 and A1). And B3 also can't be in the top 3 because it is slower than B2 and B1 (and thus is also slower than A1). So let's further update our table: A1 B1 C1 A2 B2 A3 We actually already know that A1 is our fastest horse (since it directly or indirectly beat all the remaining horses). So now we just need to find the other two fastest horses out of A2, A3, B1, B2 and C1. So for our 7th race, we simply race these 5 horses, and the top two finishers, plus A1, are our 3 fastest horses.
94.11 %
43 votes

Similar riddles

See also best riddles or new riddles.

logic

Valuable object send by mail

Suppose you want to send in the mail a valuable object to a friend. You have a box which is big enough to hold the object. The box has a locking ring which is large enough to have a lock attached and you have several locks with keys. However, your friend does not have the key to any lock that you have. You cannot send the key in an unlocked box since it may be stolen or copied. How do you send the valuable object, locked, to your friend - so it may be opened by your friend?
Send the box with a lock attached and locked. Your friend attaches his or her own lock and sends the box back to you. You remove your lock and send it back to your friend. You remove your lock and send it back to your friend. Your friend may then remove the lock she or he put on and open the box.
90.26 %
43 votes

logicshort

Difficult pop quiz

A teacher decides to give a pop quiz one day but all of her students refuse to take the quiz thinking that the teacher will call off the quiz. She can give only one of these students a detention for skipping the quiz. All of the students know each other’s names and if a student knows he/she is getting a detention they take the quiz. How can she threaten her students with the single detention so they all take the quiz?
She tells them that she will give the student who skips the quiz whose name comes first alphabetically a detention. This student won’t skip because they know they are getting a detention if they do. The next person alphabetically will then know that they will get a detention so they won’t skip either, and so on.
89.81 %
41 votes

logicshortwhat am I

It will follow you

If will follow you for 1000 miles but not miss home. It desires neither food nor flowers. It fears not water, fire, knives, nor soldiers. But it disappears when the sun sets behind the western mountains. Who Am I?
Shadow.
90.67 %
45 votes

cleanlogicshort

An empty box

How many apples can you put in an empty box?
Zero. When you put an apple, it no longer remains empty.
92.86 %
35 votes

logicmath

Strange Miles

You are somewhere on Earth. You walk due south 1 mile, then due east 1 mile, then due north 1 mile. When you finish this 3-mile walk, you are back exactly where you started. It turns out there are an infinite number of different points on earth where you might be. Can you describe them all? It's important to note that this set of points should contain both an infinite number of different latitudes, and an infinite number of different longitudes (though the same latitudes and longitudes can be repeated multiple times); if it doesn't, you haven't thought of all the points.
One of the points is the North Pole. If you go south one mile, and then east one mile, you're still exactly one mile south of the North Pole, so you'll be back where you started when you go north one mile. To think of the next set of points, imagine the latitude slighty north of the South Pole, where the length of the longitudinal line around the Earth is exactly one mile (put another way, imagine the latitude slightly north of the South Pole where if you were to walk due east one mile, you would end up exactly where you started). Any point exactly one mile north of this latitude is another one of the points you could be at, because you would walk south one mile, then walk east a mile around and end up where you started the eastward walk, and then walk back north one mile to your starting point. So this adds an infinite number of other points we could be at. However, we have not yet met the requirement that our set of points has an infinite number of different latitudes. To meet this requirement and see the rest of the points you might be at, we just generalize the previous set of points. Imagine the latitude slightly north of the South Pole that is 1/2 mile in distance. Also imagine the latitudes in this area that are 1/3 miles in distance, 1/4 miles in distance, 1/5 miles, 1/6 miles, and so on. If you are at any of these latitudes and you walk exactly one mile east, you will end up exactly where you started. Thus, any point that is one mile north of ANY of these latitudes is another one of the points you might have started at, since you'll walk one mile south, then one mile east and end up where you started your eastward walk, and finally, one mile north back to where you started.
93.84 %
41 votes

logicmathshort

Magic number

Ramanujan discovered 1729 as a magic number. Why 1729 is a magic number ?
It can be expressed as the sum of the cubes of two different sets of numbers. 10^3 + 9^3 = 1729 and 12^3 + 1^3 = 1729
90.47 %
44 votes

cleanfunnylogic

Question's wallet

After recent events, Question Mark is annoyed with his brother, Skid Mark. Skid thought it would be funny to hide Question's wallet. He told Question that he would get it back if he finds it. So, first off, Skid laid five colored keys in a row. One of them is a key to a room where Skid is hiding Question's wallet. Using the clues, can you determine the order of the keys and which is the right key? Red: This key is somewhere to the left of the key to the door. Blue: This key is not at one of the ends. Green: This key is three spaces away from the key to the door (2 between). Yellow: This key is next to the key to the door. Orange: This key is in the middle.
The order (from left to right) is Green, Red,Orange, Blue, Yellow. The blue key is the key to the door.
91.22 %
48 votes

animallogic

Frog in a well

A frog is at the bottom of a well. It is a 30 foot climb to get out. Each morning, the frog jumps 3 feet up the path out, but each night, as it sleeps, it slips back 2 feet down. Thus, at the beginning of the first day, the frog has 30 feet to go, at the beginning of the second day it has 29 feet to go, and so on. How many days does it take the frog to get out of the well?
It takes 28 days for the frog to get out (it gets out on the morning of the 28th day). This is because on the beginning of the 28th day, the frog has 3 feet left to travel. Because the frog jumps 3 feet forward each morning, it will jump out of the well on this day.
90.04 %
42 votes

logicshort

Egyptian coin

An archeologist claims he found a Roman coin dated 46 B.C. in Egypt. How much should Louvre Museum pay for the coin? Note: Roman coins can really be found in Egypt
Nothing. That coin is as phony as a three dollar bill. In 46 B.C., they wouldn't have known how many years before Christ it was.
93.39 %
38 votes