You incorrectly stated both the problem and the solution. Here is the way the problem shoul’ve been written:
You’re sitting at a table with a bunch of pennies on it. Some are heads up and some are tails up. You’re wearing a blindfold, and you’re wearing mittens so that you can’t actually feel the coins and tell which side is facing up
I tell you that a certain number of the pennies are facing heads up. Let’s say 10 are facing heads up.
With your mittens on, you can move the pennies around, you can pick them up, you can put them down again, you can shake them, you can do whatever you want.
Here’s the question: Is it possible to separate those pennies into two groups, so that the number of heads up in one group will equal the number of tails up in the other group?
Here’s the answer. You don’t know how many coins are on the table, but I’m telling you that ten are heads up. From that big group, take ten coins. Slide them over so that you have a little group of ten coins in front of you. And the larger group of coins is another pile somewhere else on the table.
What if you had, by luck, chosen all tails? Where would all the heads be? Answer: in the other pile, the big group. So how would you make the number of heads in one group equal the number of tails in the other group?
It turns out that no matter how many heads you manage to get out of the big group, the tails in the little group will always be a number equal to the remaining heads in the big group.
Let’s say, for example, that you pull out ten coins and nine of them are tails. Only one is a head. Question: How many heads are left in the big group?
Answer: nine. Thus there are nine tails in the little group and nine heads in the big group. The numbers are equal.
Now let’s say of your ten coins, you get eight tails and two heads. How many heads are left in the big group?
Answer: eight. Also, since you have eight tails in the little group, the numbers are equal.
Try again. Let’s say that of the ten coins, you get four tails and six heads. How many heads are left in the big group? Answer: four. You have four tails and the larger group has four heads. The numbers are equal.
A final example. You get one tail and nine heads. How many heads are left in the big group? Answer: one. The numbers are equal.