Color of Bear Puzzle

A Bear has fallen from a height of 10m from ground. It reached ground in sqrt(2) seconds. Luckily it didn’t get hurt. What color is the bear?

Solution

Ans - White

Explanation-

As per equation 

S=(1/2)g(t^2)

g=(2S)/(t^2)

here in question S = 10, t = sqrt(2)

so after calculation we get g = 10;

This is the maximum value of gravity and occurs on the Poles (South pole and north pole).

So color of bear is white since it is Polar Bear.

Burning Ropes with Time Measurement

Problem : There is this special kind of ropes made from some non-homogeneous material. Because of this special material, the rope takes exactly one hour to burn if lighted from one end. However, as the material is not uniform across the rope, different parts of rope may take different amount of time. So for example, one half may take 1 minute where as other half may take 59 minutes to burn.

you are given two such ropes  and you need to measure

1. 1hr

2. 45 minute

3. 30 minute

4. 15 minute

Solution

1. If we burn a single rope then we can measure 1 hr.

2. Burning of two ends of it at the same let you you measure 30 minutes.

3. Now start by lighting both ends of one rope and one end of other rope. when first rope is finished burning(in 30 minutes) then light other end of second rope ,in this way second rope half second rope is already burned so it will take more 15 minutes with both ends burning. so you can measure 45 minutes.

4.  When second rope is done burning then already 45 minutes has elapsed. 15 minutes has elapsed after first rope has completely burnt. so you can measure 15 minutes in this case.

Divide the Cake into equal parts with only 1 cut

Question: How would you cut a rectangular cake into two equal pieces when a rectangular piece has already been cut out of it? The cut piece can be of any size and orientation. You are only allowed to make one straight cut.



Solution-

You can cut the cake by the line joining the center of the original cake and the center of the removed piece, this will divide the rectangle in exactly two pieces. We can use the fact that “any line passing through the center of a rectangle divides the rectangle in two equal pieces

100 people with sword puzzle

100 people standing in a circle in an order 1 to 100.

No.1 has a sword.
He kills next person (i.e. no. 2) and gives sword to next to next (i.e no.3).
All person does the same until only 1 survives.

Which number survives at the last?

Solution

Ans - 73

Explanation-

·         Attempt 1 : 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99

·         Attempt 2: 1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97

·         Attempt 3: 1, 9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97

·         Attempt 4: 9, 25, 41, 57, 73, 89

·         Attempt 5: 9, 41, 73

·         Attempt 6: 9, 73

·         Attempt 7: 73

Two Identical Pills each day

You are on a strict medical regimen that requires you to take two types of pills each day. You must take exactly one A pill and exactly one B pill at the same time. The pills are very expensive, and you don’t want to waste any. So you open the bottle of A pills, and tap one out into your hand. Then you open the bottle of B pills and do the same thing – but you make a mistake, and two B pills come out into your hand with the A pill. But the pills are all exactly identical. There is no way to tell A pills apart from B pills. Is it possible to satisfy your regimen and take exactly one of each pill at the same time, without wasting any pills? Give answer as below

Yes

No

Can’t say

Solution-

Yes

Exaplanation - 

1. First cut each pill and divide into two parts.

2. Take one more pill from Bottle 'A' and cut into two parts and put one part in each of group.

3. Take one one group of pills one day and another group on second day.

Light Switches in the Cellar

In your cellar there are three light switches in the OFF position. Each switch controls one of three light bulbs on floor above.
You may move any of the switches but you may only go upstairs to inspect the bulbs.
When upstairs, you cannot access the switches. What is the minimum number of times you need to go upstairs to determine the switch for each bulb?

Solution-

1. First you will turn lights switch 1 to 'ON' for few minutes and then turn 'OFF'.

2. Now turn switch 2 to 'ON'. And go upstairs.

3. There you will notice as whichever bulb is 'Off' and 'hot', that points to switch 1. the bulb which is 'ON' - is attached to switch 2. And the third bulb points to switch 3.

So we need to go upstairs only once.

Cross the Bridge - How Farmer will cross the bridge.

A farmer is returning from market, where he bought a she-goat, a wolf and cabbage.
On the way home he must cross a river.

His boat is little, allowing him to take only one of the three things.
He can’t keep the she-goat and the cabbage together (because the she-goat would eat it), nor the she-goat with the wolf (because the she-goat would be eaten).

How many minimum trips for the farmer to get everything on the other side (without any harm)?
Crossing the river counts as one trip.

Solution -

1. Farmer crosses with goat.

2. Farmer returns alone.

3. Farmer crosses with cabbage

4. Farmer returns with goat.

5. Farmer crosses with wolf.

6. Farmer return alone.

7. Farmer crosses with goat.

So finally all are on other side of bridge. And total trips by Farmer are 7.