Roll These Dice

You see here

three dice, they're just ordinary $1-6$ dice and they are rolled in the usual way to see what numbers come up.

Two dice are similar and RED and the other is GREEN, and when they're rolled you get three numbers.

What I'd like you to do is to add up the numbers on the two RED dice and then subtract the number that's on the GREEN dice.

So if one RED is $4$ and the other RED is $5$ and the GREEN is $3$ we should add together $4$ and $5$ to make $9$ and then subtract the $3$ so that gives us a final answer of $6$.

You could roll these dice over and over again and see what you get each time by doing the addition and subtraction.

It might get rather annoying as the same numbers may come up over and over again and some numbers just might not appear. Like when you're desperate for a six in a board game.

In this challenge I'd like you to consider:-

• what are all the different possibilities that could come up?
  
• what are the final answers by doing the addition and subtraction each time?
  
• is there a good way of making sure you find all the possibilities?
  
• how will you record what you've found out?
  

Now have a go!

• How many different ways have I found for the dice to land?
• Do any of them have the same answers?

Having written the questions down try answering them.

See if you can tell someone WHY the answers are what they are.

That sounds funny. Let me explain.

Suppose you ask "Do any of them have the same answers?''. You look at your results and say "Yes!'' Now you have to ask WHY are they the same?

eg.

so you'd need to say WHY these results are the same.

So have a go at answering WHY the answers that you came to from asking your own questions have happened.

Now you can ask, "I wonder what would happen if, instead, I ...?''

Enjoy this rather different challenge and please send in your results.