SOLUTION: Six hundred pennies are placed in a row. If every other penny is replaced by a nickel and every third coin is replaced by a quarter, what is the final value of the 600 coins?

We only need to look at the first 6 coins and multiply their
value by 100, because each of the 100 groups of 6 turn out
the same way.

We start with

1¢ + 1¢ +  1¢ + 1¢ + 1¢ +  1¢  + ···

Then we replace every other one with a nickel and have this:

1¢ + 5¢ +  1¢ + 5¢ + 1¢ +  5¢  + ···

Then we replace every 3rd one with a quarter and have this:

1¢ + 5¢ + 25¢ + 5¢ + 1¢ + 25¢  + ···

That last line adds to 62¢ and we
have 100 groups just like this one,
so the total amount of money is $62.

Edwin