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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# A Bit of a Dicey Problem

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### Roll These Dice

### Bipin's Choice

### Trick or Treat

Links to the University of Cambridge website
Links to the NRICH website Home page

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Age 7 to 11

Challenge Level

Look at these two dice. If you add together the numbers of dots on them, the total is $2$.

When you roll two ordinary six-faced dice like these and add together the two numbers, what results could you get?

Do you have more chance of getting one answer than any other?

If so, what is that answer? And why?

What if you use a dice with $10$ numbers on, like these?

What answers could you get now?

Do you have more chance of getting one answer than any other?

If so, what is that answer? And why?

Now try with more dice or a mixture of dice. What do you notice now?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Bipin is in a game show and he has picked a red ball out of 10 balls. He wins a large sum of money, but can you use the information to decided what he should do next?

Mrs. Smith had emptied packets of chocolate-covered mice, plastic frogs and gummi-worms into a cauldron for treats. What treat is Trixie most likely to pick out?