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# Flipping a Coin

**Flipping a Coin**

**Premise:**

- You are in a room blindfolded.
- There are 10 coins placed in front of you where, 5 of them are placed heads up and 5 are placed heads down.
- It is not possible to determine which side is up by touching them.
**Task:**- The task is to separate these coins into two piles of 5 such that both the piles have an equal number of heads up.
- You are allowed to flip the coins any number of times.

**Flipping a Coin**

**Puzzle b****ased on Flipping coin:**

You are in a room blindfolded. There are 10 coins placed in front of you where, 5 of them are placed heads up and 5 are placed heads down.

It is not possible to determine which side is up by touching them.

**Task:**

- The task is to separate these coins into two piles of 5 such that both the piles have an equal number of heads up.
- You are allowed to flip the coins any number of times.

** Solution**

**Step 1:** Take the coins and arrange them into two piles of with 5 coins each.

**Step 2:** Fixing one pile, flip all the coins in the other pile.

**Conclusion:** The number of heads in both the piles will become equal. This happens because the coins have only two probabilities, they can either have a heads or a tail.

To further simply this:-

We know that are the 10 coins :** H H H H H T T T T T**

Now, let us consider the following cases

**Case 1:**

Let us consider the coins are divided in two piles in the following order

`P1:- H T T T T and P2:- T H H H H`

Now if we flip P1, then

P1:- T H H H H

Therefore both the piles will have equal no. of heads.

**Case 2:**

Let us consider the coins are divided in the following order

`P1:- T H T H H and P2:- H T H T T`

Flip P1, it becomes

`P1:- H T H T T`

Therefore both the piles will have an equal no. of heads.

**Case 3:**

Let us consider the coins are divided in the following order

`P1:- H T H H H and P2:- T T T T H`

Flip P2 it becomes

`P2:- H H H H T `

Therefore both the piles will have equal no. of heads.

- What is happening here is that we are fixing the number of heads in one pile and in the other pile we are flipping them.
- The logic here is that the number of heads up and heads down coins are fixed in the beginning.
- When we are dividing them into two piles, if one pile gets “x” heads up then the other pile will have “x” tails up and then we flip the other pile it becomes “x” tails and the heads become tails.

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**Fox, Duck and Circular Pond Answer****Caves and a thief Answer****Couples crossing the river Answer****Distance walked to office Answer****Number game to save life Answer****Classic lateral thinking Answer****Finding the injection for anesthesia Answer****Toggling Prison cell Answer****Tic Tac Toe Answer****Magical Matrix Answer****Last Palindrome Date Answer****Number of chocolates in a bag Answer****Worm and leaves Answer****Puzzle on the idler Answer****Chain Linking Answer**

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