Races To Find Horses For Courses

What was the task? 

First we need to make 5 groups of 5 horses each. Let's put each group on race & note down rank of each horse & corresponding group. This requires 5 races.

Taking out winner of each group aside. In a next race, winner of each group run & fastest winner is found. Total 6 races are conducted till now.

Now let's name group of fastest winner as A, second fastest winner as B & so on as C, D, E. Each horse would be identified by it's group name & rank as Group.Rank. For example, B.3 means the horse that came 3rd in group B & D.5 is horse that came last in group D.

For next race, we can eliminate few. Let's remind we have to find 3 fastest horses. Now let's logically eliminate few horses. Those horse for which we are sure that at least other 3 are faster than those will be eliminated.

1. Now A.1, B.1 & C.1 are faster than D.1 & E.1. So D.1 & E.1 & respective groups eliminated straightaway.

2. The C.2 (& other members of C) eliminated as A.1, B.1, C.1 are faster ones.

3. The B.3 (& other member of B) eliminated as at least A.1, B.1, B.2 are faster ones.

4. Similarly, A.4 & A.5 have 3 horses ahead as A.1, A.2 & A.3.

5. A.1 is already proved it's fastest among all, so no need to re race by taking it.

Crossing The River In Minimum Time

Four people need to cross a dark river at night. They have only one torch and the river is too risky to cross without the torch. If all people cross simultaneously then torch light won't be sufficient. Speed of each person of crossing the river is different. Cross time for each person is 1 min, 2 mins, 7 mins and 10 mins. 

However 2 can cross together but there is one limitation.If two are crossing the river then it takes time equal to slowest person would take alone. For example, if persons with cross times 1 min & 10 mins are crossing then it would take 10 mins for both to cross the river.

What is the shortest time needed for all four of them to cross the river ? 

  
Find here the efficient way! 

Source 

Efficient Way To Cross The River

What's the challenge? 

Let's name each person by their crossing times as 1,2,7,10.

The instant solution that everyone can think of is using 1 as a usher to guide all. That means 10 & 1 goes, 1 comes back; 7 & 1 goes again 1 comes back and 2& 1 goes finally. This would take 10 + 1 + 7 + 1 + 2 = 21 mins to cross rivers.

Is it really efficient solution? What if we find a way to cross both 10 & 7 in one go & other 1 waiting across to bring back torch.

1. The 1 & 2 goes across but 1 comes back - 2 + 1 = 3 mins required.

2. Now 10 & 7 goes across & send 2 back with torch - 10 + 2 = 12 mins required.

3. Finally after coming back 2 & take 1 across the river - 2 minutes required.

So total 3 + 12 + 2 = 17 minutes required to cross the river for those 4 persons. In first step, 2 can also come back & send 10 & 7. In that case, in second step, 1 has to come back to take 2 across the river. Isn't this a more practical solution? 

Complex Time, Speed & Distance Maths

There is a circular race-track of diameter 1 km. Two cars A and B are standing on the track diametrically opposite to each other. They are both facing in the clockwise direction. At t=0, both cars start moving at a constant acceleration of 0.1 m/s/s (initial velocity zero). Since both of them are moving at same speed and acceleration and clockwise direction, they will always remain diametrically opposite to each other throughout their motion.

At the center of the race-track there is a bug. At t=0, the bug starts to fly towards car A. When it reaches car A, it turn around and starts moving towards car B. When it reaches B, it again turns back and starts moving towards car A. It keeps repeating the entire cycle. The speed of the bug is 1 m/s throughout.

After 1 hour, all 3 bodies stop moving. What is the total distance traveled by the bug?

Find out complex calculations here!

Simple Solution of Complex Problem

Here is that complex looking problem! 

Everything built, written or designed in the given problem is to distract you from basic physics formula.

Speed = Distance / Time

Hence,

Distance = Speed x Time 

All the details given except speed of bug & time for which it traveled are there to confuse you. Speed of bug is 1 m/s & it traveled for 1 hour = 3600 seconds.

Distance = 1 x 3600 = 3600 m

So the total distance traveled by the bug is 3600 m.