Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has ten iron coins and ten copper coins, how many different sums from 1¢ to 70¢ can he make with a combination of his coins?

It can be made 66 combinations.

Explanation:

Total amount of possibilities = 10*5¢+10*2¢=70¢

The first combination 1¢ cannot be made because 2¢ is not divisible.

The second combination is 2¢. (Possible)

The third combination 3¢ cannot be made for the same reason.

There are no possible combinations for 1¢ and 3¢.

The same happens with 67 and 69.

For example:

66¢ = 10*5¢+8*2¢

Next combination will be:

68¢ = 10*5¢+9*2¢

And finally:

70¢ = 10*5¢+10*2¢

So there are 4 combinations that are not possible.

The total amount of possible combinations are:

70-4=66 combinations