Snailing on puzzles

1. What is the next number in this sequence?
1, 11, 21, 1211, 111221, ???

Solution:
Each number in the sequence describes the previous one.
i.e. first number= 1
second number = one one = 11
third number = two ones = 21
fourth number = one two and one one = 1211 and so on
so the sixth number will be 312211

2. You’ve got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?

Solution:
For this kind of questions , break the bar with the values 1, 2 , 2^2 , 2^3 , 2^4……. i.e in the series of 2^n where n = 0 to n. This combination always have all the natural number values possible upto the total value of bar.

Here it will be accordingly 1, 2 ,4 break
Now day 1, give 1
Day 2, give 2 take 1
Day 3 give 1
Day 4, give 4 take 1,2
Day 5 give 1
Day 6, give 2 take 1
Day 7 give 1

3. You have 5 jars of pills. Each pill weighs 10 gram, except for contaminated pills contained in one jar, where each pill weighs 9 gm. Given a scale, how could you tell which jar had the contaminated pills in just one measurement?

Solution:
Take 1 pill from jar 1 , 2 from 2^nd , 3 from 3^rd , 4 from 4^th and 5 from 5^th.
If they all had 10gm pills these pills weigh 150 gms. If jar number n has contaminated pills we have total sum = 150 – n gms. As per pill 1 gram is reduced and we took out n pills from nth jar, so loss in gms = n. And hence it is the nth jar. That means the decrease in value measured drom 150 is the jar number with contaminated pills

4. Bridge
There are 4 people on a side of a bridge. They all have to go to the other side of the bridge. They have a lantern that will last for 17 minutes which is necessary to cross the bridge. Bridge can support only 2 people at once. Having their own individual maximum speed, they can cross the bridge in 1, 2, 5 and 10 minutes respectively. What combination they should use to cross the bridge in time.

Solution:
Here we must ensure that the two slowest persons should not come back to give back the lantern as they will consume the maximum time. To make that possible have the one of the faster persons on the other side every time we need to bring back the lantern. Do this by:

1 and 2 cross the bridge ——- time taken = 2 min
1 comes back ——————–time taken = 3 min
5 and 10 cross ——————-time taken = 13 min
2 comes back ——————–time taken = 15 minutes
1 and 2 cross the bridge ——–time taken = 17 minutes

5. You are standing outside the first floor entrance to a building. Next to you is a bank of 3 light switches. One of the switches controls a light bulb in a stock room on the second floor. The other two switches don’t control anything. The only way you can check the light on the second floor stock room is to physically walk up the stairs, open the door to the stock room, and check the light. You can do anything to the switches that you want before you walk up the stairs; however you are allowed only one trip up the stairs to check the light. Assuming the light and switches are off to start with, how do you find out which light switch controls the light using only one trip to the room?

Solution:
Needs a little bit of knowledge that bulb get hot when turned on for a while
Turn on the first switch and wait for sometime. Then turn it off and turn on the second.
Move immediately to the room. There can be three cases :
Hot and off bulb — 1^st switch
Cold and glowing bulb — 2^nd switch
Cold and off bulb — 3^rd switch

6. You are on one side a river and need to cross with your dog, chicken and some grain. There is a boat but it is so small it will only be able to carry yourself and one of the items at a time. If you leave the dog and chicken together the dog will chase the chicken away. If you leave the chicken with the grain the chicken will eat the grain.
How do you get yourself and the three items across the river?

Solution:
Dog, chicken, you, grains >>>>>>>>>>>
Dog, grains <<<<<<<<<<<<<<<<<<<< you, chicken
Dog, grains, you >>>>>>>>>>>>>>> chicken
Grains <<<<<<<<<<<<<<<<<<<<<< chicken, you, dog
Grains, you, chicken >>>>>>>>>>>>>>> dog
Chicken <<<<<<<<<<<<<<<<<<<<<< you, dog, grains
Chicken, you >>>>>>>>>>>>>>> dog, grains
—————————————— Dog, chicken, you, grains

7. You are presented with three closed boxes, labeled “Apples”, “Oranges“, and “Apples and Oranges“. Y are told that all the labels are wrong. By looking at a single fruit from one box you can correctly label the three boxes. How?

Solution:
There can be two ways of wrong labeling
1. Original oranges — apples, Original apples — Both, Original both — oranges
2. Original oranges — both, Original apples — oranges. Original both — apples
So pick one from the one labeled both. If it is an oranges then it’s the first case else it’s the second case

8. Given a rectangular cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife?

Solution:
Join the centers of the original and the removed rectangle. And cut along that line.

9. Cut a circular cake in 8 equal pieces with 3 straight cuts permitted.

Solution:
There is a catch!! Cut at ninety degrees using 2 cuts and then horizontally from the height (remember circular cake is a cylinder)

10. If you had an infinite supply of water and a 5 litre and 3 litre jars, how would you measure exactly 4 litre without extra jar?

Solution:
Fill 5 litre jar and pour 3 litre in the 3 litre jar. Now you have 2 litres remaining in the 5 litre jar. Now empty the 3 litre jar and pour that 2 litres in the 3 litre jar. Now fill 5 litre jar and pour it in the 3 litre jar containing 2 litres already. It can accommodate only 1 more litre. So remaining in the 5 litre jar is 4 litre