You are given 10 coins, out of which 5 coins have heads facing up and 5 coins have tails facing up. You are blindfolded, so you cannot see or feel which side of the coins is facing up. Your task is to split the coins into two groups, with each group having the same number of coins showing heads. You can flip as many coins as you want but cannot peek to see which side is up.

Objective:
Divide the 10 coins into two groups such that each group has the same number of heads facing up.

Solution:

This puzzle seems tricky because you can’t see the coins, but there is a clever way to solve it using the properties of flipping coins.

Step-by-Step Solution for 10 Coins Puzzle:

Step 1: Divide the Coins into Two Groups

The first step is to simply divide the 10 coins into two groups of 5 coins each. You don’t need to know which coins are heads or tails at this point—just randomly split them into two groups.

Step 2: Flip All Coins in One Group

Now, flip all 5 coins in one of the groups. It doesn’t matter which group you choose; just flip every coin in that group.

Step 3: Why This Works

This strategy works because of the way flipping coins affects the number of heads. Let’s break it down:

• Assume in the first group of 5 coins, there are X heads (where X can be any number from 0 to 5). This means the second group must have 5 - X heads, since there are 5 heads in total between the two groups.
• When you flip all the coins in the first group, all heads become tails and all tails become heads. Therefore, the number of heads in the first group after flipping will be 5 - X.
• Now, both groups have 5 - X heads, which means the two groups have an equal number of heads.

For example:

• If the first group originally had 2 heads and 3 tails, after flipping, it will have 3 heads and 2 tails.
• The second group, which originally had 3 heads, will still have 3 heads.
• Now both groups have exactly 3 heads each.

Final Answer

To solve the puzzle, divide the 10 coins into two groups of 5 coins each, and then flip all 5 coins in one of the groups. This guarantees that both groups will have the same number of heads.