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Lavesh, Bolt, and Lewis race each other in a 100 meters race. All of them run at a constant speed throughout the race.
Lavesh beats Bolt by 20 meters.
Bolt beats Lewis by 20 meters.
How many meters does Lavesh beat Lewis by ?
Know here the answer!
Source
What was the question?
Let Lavesh's speed be 10 m/s. Then he must have taken 10 seconds to finish the race. Since Bolt was beaten by Lavesh by 20 m he must have run 80m when Lavesh finished race in 10 seconds (t=10). So his speed would be 8 m/s.
Now Bolt requires 100/0.8 = 12.5 seconds to finish the race. When he finished, Lewis was 20m behind i.e. 80m from starting point at t = 12.5. So Lewis speed is 80/12.5 = 6.4 m/s
At t = 10 seconds, when Lavesh finished his race Lewis must be at 6.4 x 10 = 64 m from starting point. Hence Lavesh beats Lewis by 100 - 64 = 36 m.
Another method.
Let L be the speed of Lavesh, B be the speed of Bolt & W be that of Lewis. Then,
L/B = 100/80 = 5/4
L = (5/4) B .......(1)
Similarly,
B/W = 100/80 = 5/4
B = (5/4) W .......(2)
Putting (2) into (1),
L = (5/4) x (5/4) W
L/W = 25/16
L = (25/16) W
For given time t, when Lavesh finished the race,
Distance by L/ Distance by W = 25 / 16
100 m/ Distance by W = 25 / 16
Distance by W = (16 x 100) / 25 = 64.
So when Lavesh finished cross line at 100 m, Lewis was at 64m i.e. 36m behind. In other words, Lavesh beats Lewis by 100 - 64 = 36 m.
You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.
The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.
You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.
You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.
What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?
Here is the test designed for it!
Source
Here is the challenge for us!
Here binary number system can come to rescue. Just for a moment, let's assume there are 15 bottles. Now let's number the bottles from 1 to 15. To test these 15 bottles we need 4 prisoners as below. Let's number the prisoners from in descending 4 to 1.
Wherever 1 is written for the particular bottle number, that bottle should be given to particular prisoner. Otherwise should not.
So for the specific bottle with unique number a specific combination of prisoners (they are bits here) would be formed.
For example, if bottle labeled as 11 has a poison then prisoner no. 4,2,1 would die. In other words, if prisoner 4 & 2 die then the bottle no. 10 had poison.
For 16th bottle we would have needed 1 more prisoner.
In similar way, to test 1000 bottles, we need 10 prisoners (2^10=1024). Depending on what combination of prisoner die we can determine which bottle had poison. If prisoners numbered from 10 to 1 & if prisoner 10,8,6,3 & 2 die then bottle no.678 (binary - 1010100110) must had poison. Since the poison takes some time to take effect, even if prisoners taste this bottle, we still would have time to test rest of all bottles in given binary pattern.
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| Poisonous Bottle |
In case there were 1025 bottle, we would have needed 11 prisoners.
