Posted by **Nicki** on Monday, April 25, 2011 at 3:02pm.

Suppose there are 500 pennies in a row... (math problem)?

The pennies are all "heads up"

Now suppose that 500 people line up and ...

Person #1 turns over all the pennies

Person #2 turns over every 2nd penny, starting with penny number 2

Person #3 turns over every 3rd penny, starting with penny number 3

Person #4 turns over every 4th penny, starting with penny number 4

etc..

After everyone has gone through the line, which pennies will show "tails"?

- Math -
**MathMate**, Monday, April 25, 2011 at 3:28pm
This has to do with the number of factors of numbers.

For example, 6 has 4 factors: 1,2,3,6

Note how neatly the outermost factors (1,6) multiply to give 6, and the inner set (2,3) also.

You will note that almost all numbers, prime or composite, have an even number of factors, hence almost all coins will be turned over an even number of times, which in turn makes them remain "head".

The only exceptions are perfect squares, such as 1,4,9,16,...

For example, 16 has factors:

1,2,4,8,16 (note: 1*16=16,2*8=16,4*4=16).

where 4 is actually twice, but with an odd number of factors.

Therefore, the only coins that remain "tails" up are the perfect squares.

See also a previous discussion on a similar problem:

http://www.jiskha.com/display.cgi?id=1298342653

## Answer This Question

## Related Questions

- math - Jenny places 100 pennies on a table, with 30 showing heads and 70 showing...
- maths - Class 5G is having a pizza party. Mrs Baker asked all the children to ...
- math - A child's coin bank contains $2.58 in pennies and nickels. If the number...
- math - suppose you wanted to place 1,000,000 pennies in large coin banks. If you...
- math - HELP HELP I need to work this questions. Six hundred pennies are placed ...
- math - Mary has 6 more pennies than Andy has. Together they have 28 pennies. How...
- math - suppose you wanted to place 100,000 pennies in large coin banks. If you ...
- math - Petra and Yelyenna begin with same number of pennies. After Petra gives ...
- math - Suppose u want to place 1,000,000 pennies in large coin banks. If u put ...
- MATH - Suppose you wanted to place 1,000,000 pennies in large coin banks. If you...

More Related Questions