### #1 - Clock Riddle

What Time Should the last watch show ?

5:19 Starting with the watch on the left, add 42 minutes to the time shown to give the time on the next watch to the right

What Time Should the last watch show ?

I have two rectangular wires.

Both of them have property that when i light the fire from one end , it will take 60 minutes to get completely burn.

However they do not burn at consistent speed (i.e it might be possible 1st 20% burn in 50 minutes and 80% can burn in 10 minutes).

So how could i measure 45 minutes ?

Steps:

A) burn 1st wire from both end and 2nd wire from one end

B) After 30 minutes(when 1st wire gets completely burned out) , burn the second wire from 2nd end as well

C) when 2nd run completely gets burned , you know its 45 minutes.

I have two sand hour glasses:

1. A 7 minute one and

2. An 11 minute one.

Using just these 2 sand hour glasses, how can i measure time as 15 minutes ?

1. Start both the 7 minute hour glass & 11 minute hour glass.

2. Wait till the 7 minute hour glass times out. Time is 7 minute!

3. Restart the 7 minute hour glass. At this time 11 minute hour glass will have 4 minutes left to time out.

4. As soon as 11 minute glass times out invert the 7 minute hour glass. Total time now is 11 minutes.

5. After inverting 7 minute hour glass, it will now have 4 minutes left for time out.

6. After these 4 minutes times out, the total time is 15 minutes.

Time in a digital clock can be palindromic like 12:12 (same when read forwards or backwards).

Whats the minimum interval between 2 times that are palindromic ?

2 minutes (between 9:59 and 10:01)

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

17 mins

The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 mins. Is that it? No. That would make this question too simple even as a warm up question.

Let’s brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let’s put all this together.

1 and 2 go cross

2 comes back

7 and 10 go across

1 comes back

1 and 2 go across (done)

Total time = 2 + 2 + 10 + 1 + 2 = 17 mins

A large water tank has two inlet pipes (a large one and a small one) and one outlet pipe. It takes 3 hours to fill the tank with the large inlet pipe. On the other hand, it takes 6 hours to fill the tank with the small inlet pipe. The outlet pipe allows the full tank to be emptied in 9 hours.

What fraction of the tank (initially empty) will be filled in 0.64 hours if all three pipes are in operation? Give your answer to two decimal places (e.g., 0.25, 0.5, or 0.75).

In one hour,

Soln 1:

the large inlet pipe fills 1 / 3 of the tank;

the small inlet pipe fills 1 / 6 of the tank;

the outlet pipe empties 1 / 9 of the tank; and therefore

all three pipes together fill [ (1 / 3) + (1 / 6) − (1 / 9) ] of the tank.

Fraction of the tank that will be filled in 0.64 hours =

0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.

Soln 2:

Let V be the total volume of the tank. From equation (1),

Flow Rate (large inlet pipe) = V / 3

Flow Rate (small inlet pipe) = V / 6

Flow Rate (outlet pipe) = V / 9.

Substituting in equation (2),

Rate of Accumulation in tank = (V / 3) + (V / 6) − (V / 9).

Using the above result in equation (1),

Time required to fill the complete tank = V / [ (V / 3) + (V / 6) − (V / 9) ].

Note that V cancels out on simplifying the above expression.

Fraction of the tank that will be filled in 0.64 hours =

0.64 [ (1 / 3) + (1 / 6) − (1 / 9) ] = 0.25.

I noticed that in my big wall clock , there is a time when the minute and hour clock are exactly between one and two.

Also i notice both hands lie on top of each other.

What is the time i am talking about ?

12:00

both minute and hour clock lie exactly between the number one and two in the number

I possess two wires. Both of them have an inconstant thickness but both of them burns completely in sixty minutes. The problem is that I want to measure forty-five minutes while using these two wires.

How can I measure if cutting the wire in half is not possible due to non-homogeneous construction ?

45minutes

It is not as hard as it seems. I will burn one wire on both ends and the other wire at one end only. The first wire will burn completely in thirty minutes and at that very moment, I will burn the other end of the second wire and it will burn in fifteen minutes. Thus both of the wires will be burnt in 30 + 15 = 45 minutes.

You are frying fishes on a pan which can accommodate only 2 fishes at one time. It takes 5 minutes to fry one side of the fish.

What is the shortest time in which you can fry 3 fishes in the same pan ?

15 minutes.

Put 2 fishes in the pan. Fry for 5 minutes and then take out one and turn the other one. Also put in the third fish. Now fry for 5 minutes. The fish that you turned must be ready now so take it off while turning the other one. Also put in the fish which was fried from one side only in the pan. Fry them for 5 minutes and all the three fishes are fried now.

man gave one son 10 cents and another son was given 15 cents. What time is it?

1:45.

The man gave away a total of 25 cents. He divided it between two people. Therefore, he gave a quarter to two