Question

Lets say you have a bunch of pennies that you are dividing into different groups. How many pennies could you have when you break the pennies into groups of 2 , you have 1 penny left over

Answer 1

Answer: We have an odd number of pennies.

Step-by-step explanation:

So we have N pennies.

When we wan to divide the N pennies into groups of 2, we have a penny left over.

This means that N is not divisible by 2.

The problem is that there are infinite natural numbers that are not divisible by two, this is the set of odd numbers.

And remember that an odd number can be written as:

N = 2*k + 1.

where k is an integer.

Then we want to divide this by 2 (divide N into groups of 2)

we have:

N/2 = (2*k + 1)/2 = 2*k/2 + 1/2 = k + 1/2.

So we have k groups of 2 pennies, and a penny leftover that we can not divide into two.