Two Beautiful Puzzles

Let’s solve two beautiful puzzles today both of different kind and very interesting. The similarity between the two puzzles is that when you know the answer, they will seem very obvious to you but I can bet it will take some time to get to the answers. If you are able to solve them by yourself, a sense of triumph is guaranteed. So enjoy solving the puzzles.

Puzzle 1: The two Eggs

There is a building of 100 floors (1-100) and you have two eggs with you. You want to find out the minimum floor (we will call it “the floor”) from top of which if you drop the egg it will break. So you have to come up with a strategy by which you can definitively find out the floor with minimum number of drops. You can use the same egg again if it’s not broken. So you have to tell the maximum number of drops required to find out the floor by your strategy and it should be minimum.

Hint: If you have one egg then you need 100 drops to find the floor, because the strategy will be to start with floor 1 and then go to floor 2 and so on. You can’t just go directly to any of the higher floor because if the egg breaks then you can’t find out the floor. But with two eggs you can do some jumping on the first place and use the second egg for deterministically find out the floor.

Puzzle 2: 5 pirates and 100 coins

Once a group of 5 pirates got 100 gold coins from a dead ship. They wanted to distribute these coins among them. So they set some rules before start dividing. The pirates were A, B, C, D and E from eldest to youngest respectively. i.e. A is the eldest and E is the youngest. All the pirates are intelligent and very greedy.

The Rules are:

First A, the eldest will propose how to  distribute the coins, then if half or more than half including A gets agree to the proposal then the coins will be distributed according to A’s proposal but if it’s less than half then A will be killed. Now B will propose his proposal, and similarly if half or more than half including B agree to the proposal then the coins will be distributed according to B or else he will be killed and then it’s turn of C and so on.

What is the maximum number of coins A can take with his clever proposal?

Hint: very tricky hit the root and don’t ignore any information in this puzzle except the dead ship.

Triumph 1:

I know you must be having some number by your strategy, so let me share the answer with you before I discuss how. Answer is 14

Almost everyone whom I have asked this puzzle, takes some time to understand what I am asking for, is it the floor or the strategy or the minimum number of drops. It’s actually very hard to phrase this puzzle simpler. I tried but I think many would still be having the same problem.

When asked this puzzle most of us start with the first drop from and arbitrary number mostly a number between 10 to30 sometimes its 50. Then we think if it does not break then where and we move ahead, and then when we approach 100 we start thinking if it breaks then what. After 5 iteration almost everyone reaches to an answer of 19 or 20, with a strategy of dropping the first egg at 10,20,30 and so on and if it breaks at 100 then start from 91 and reach to an answer of 19. Then people ask for the answer and if i say the answer some people really fight hard to reach to the answer and then realise it’s the answer.

Let’s say the answer is N.

1^st Drop: So the maximum floor from which I can drop for the first time is N, so that if it breaks I can use the remaining one to cover from 1 to N-1.

2^nd Drop: As I lost one drop at N, now I have to find out the floor in N-1 drops, so I can drop at [N+(N-1)]^th floor, so that if it breaks I can use the remaining egg to cover the floors N+1 to [N+(N-1)]-1

3^rd Drop : N+(N-1)+(N-2) and so on

So at the end we have to drop the egg from N+(N-1)+(N-2)+…+2+1 which is ∑N

So if we have to cover 100 floors, ∑N≥100 and N to be minimum makes N=14

So we will drop the first egg from 14^th floor if it breaks we will start from 1^st floor and within 14 drops we can find the floor and if does not break at the 14^th floor then we will drop at 27^th (14+13) floor, and if it breaks we will start from the 15^th and so on.

I consider this puzzle as a classic puzzle which teaches multiple things about puzzle solving. The concept of N is a number, in puzzles like this you can assume the answer to be N and start solving like you solve an equation for the value of N. Also this is a classic example where we start with hit and trial and then we realise the constraints of this puzzle, and I feel there is nothing wrong with hit and trial as long as you are getting something out from every heat and trial and moving towards the goal. We use many kinds of search algorithms; binary search is the most famous and most applied search algorithm. This puzzle also tells something about a new search algorithm, I named it Broken-Egg search; we can increase the number of eggs to reach to the result faster. I also used this search algorithm in one of my project where it was difficult to use binary search. If at any point of time you find difficulty in implementing binary search you can try this search algorithm.

PS: Try solving the same puzzle if you have 3 eggs

Triumph 2:

This is a very common puzzle but for those who never heard of this puzzle, it’s the Unthinkable, because this puzzle has no start point. Also the information given in this puzzle seems not so useful. Even it’s almost impossible for 95 percent of the people to get to the answer without any prior experience on these kinds of puzzles. Let’s start with the solution

A proposes: need 2 more people among B, C, D and E to agree with A’s proposal

As we can’t justify with certainly who will support A with how much coins, so it’s of no use putting forward our stupid figures of 33,34,20,25 etc.

So let’s find out where is the bottom, if everyone else is killed and it’s a matter between D and E, then D will take all the coins without giving E anything. So E knows that when the thing will come down to this he will not get anything. Lets see what happens one step up with C, D and E as everyone is so much intelligent and greedy so C will just give one coin to E and E will support as he finds one coin or else will get nothing if C get killed. So C can maximum take away 99 coins. Moving to B, C, D and E B will give one coin to D and take 99. D will support B with one coin as D will get nothing if B gets killed. So when all are there A will give C and E one coin each and take 98 with him because B can play his trick where C and E gets nothing.

Answer to the puzzle is 98

Some obvious arguments : people many a time ask me why E will say yes when he is getting the same from C, but E is so much intelligent that he can see B’s proposal getting succeed, in that case it will not come down to C, so E is playing safe.

This puzzle really puzzles me a lot, because I still wonder will this happen in a real life, Because 99% guys who heard this puzzle for the first time didn’t able to answer it. Does the solution is a perception or a paradox Or is there a catch in the solution which we are not able to discover. Logically till day I am convinced with this solution. I think in real life we are much more greedier than the pirates are in the puzzles, and the greediness makes us blind from analysing the real consequences, so the puzzle with a constraint that all are intelligent and greedy is quite not true in real life. Also in Real life we think of bending decisions by bribing, like B can bribe C and E more than one coin and get them against A but in puzzles until and unless told you can think of things like that. Because its strictly mentioned A will propose first then B, so B can’t play around before A. I think this is a big factor in our inability to answer the puzzle. We think of everybody at the same time we think of A, B, C.. every pirate purposing at same time and get confused. There is a lot more psychology involved behind this puzzle. your inputs are very much necessary.

PS: Try to solve the puzzle with 5 coins and 100 pirates, you have to tell who will definitely die?

Participate actively in this blog I promise an entertaining time ahead.

Thank You !