iced_tea wrote:

can you please show your work ?

The possible â€˜toeâ€™ (sum) values for the 3 dices are 3 to 18.

Now, there is 1 way of getting toe = 3 ( 1,1,1)

3 ways of getting toe = 4 (1,1,2 : arranged in 3 ways for 3 dices)

6 ways of getting toe = 5 (1,2,2; 1,1,3 : arranged in 3 ways each)

:

3 ways of getting toe = 17 (6,6,5 : arranged in 3 ways)

1 way of getting toe = 18 (6,6,6)

If you notice the number of ways of getting toes is increasing in geometric progression. Similarly if you go in descending order from 18 , the number of ways again increase in geometric progression. And it seems the maximum ways of getting any sum is 18.

So the possible ways of getting toes = 3 to 18 are as follows:

Toe = 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Ways = 1 3 6 9 12 15 18 18 18 18 15 12 9 6 3 1

In order to win. Joe needs to get the sum on 3 dices between 11 to 18 (both inclusive). And as you can see there are 50% ways of doing that.

But I think there should be a better way of doing it, because it took me 20 minutes to just figure out the pattern for the number of ways of getting all toe values.