100 pennies: Ask Marilyn - Oct 21 Parade Magazine?

Question

100 pennies are on a table, and exactly 10 are tails. With
your eyes closed, separate them into two groups so that
each group has the same number of tails. Her answer is to
take any 10 pennies and turn them over; that is group 1,
and it has the same number of tails as the remaining 90.

Why does this answer work?

Answer 1

Suppose the 10 pennies we pick have x heads and
y tails. Then there are 10-y tails left in the group
of 90 pennies and x + y = 10, so y = 10-x tails in the
group of 10.
Now flip the coins over and now there are y heads
and x tails. But now x = 10-y, so both groups
now have the same number of tails.
Numerical example.
Suppose our group of 10 has 6 heads and 4 tails.
Then there are 6 tails left in the group of 90.
If we flip our group of 10 over we now have
4 heads and 6 tails, so each group has 6 tails.
Hope that makes sense!

Answer 2

Because you are changing all of them to the opposite, nothing really changes.

If you took:

1 tail, leaving 9 of the 90, after turning your ten, your 9 heads would become 9 tails, same as the larger group.

2, leaving 8, after turning you have 8 tails...and so on...

Answer 3

Ask Marilyn

Answer 4

I dunno, I didn't get that one either. The answer didn't make any sense.