Challenge Level

There are three dice, each of them with faces labelled from 1 to 6.

When the dice are rolled they can be combined in six different ways to make a number less than 10 with two decimal places.

For example, if I roll a 2, a 3 and a 6, I can combine them to make 2.36, 2.63, 3.26, 3.62, 6.23 or 6.32.

Now round each of these numbers to the nearest whole number:

2.36 rounds to 2, 2.63 rounds to 3, 3.26 rounds to 3, 3.62 rounds to 4, 6.23 rounds to 6 and 6.32 rounds to 6.

Repeat for other rolls of the dice.

Can each of the six numbers round to the same whole number?

Can each of the six numbers round to a different whole number?

There are some interactive dice here that you can use for this problem.