Question

How many different sums are possible
when two adjacent sides on a standard die are added together?

Answer 1

brute force, 12?

Answer 2

Too many, thnk again. We always get these types of questions on tournament tests so I thought it would help to practice a few of them. I wish the others would join in.

Answer 3

Hint: Recall that the opposite faces of a die always add to 7.

Answer 4

how come they always add to 7?

Answer 5

6 then?

Answer 6

@romoore93 -> I don't know.

Answer 7

36?

Answer 8

Woah! way too many @romoore93

Answer 9

so they can only add up to 7 does that mean how many possibilities they are that add up to 7 from the 2?

Answer 10

@dpalnc --> Post the 6 you have and maybe we'll be able to get the others.

Answer 11

actually i didn't even realize that opposite faces sum is 7 on a standard die. wow, i learn something new everyday!

Answer 12

that means if wasn't standard, the answer to this question would be different then

Answer 13

@romoore93 --> A "die" is a single number cube, not the pair of dice.

Answer 14

This is a standard die --> when two adjacent sides on a standard die ...

Answer 15

Here are all the connections:

1-2,1-3,1-4,1-6

2-6,2-1,2-3,2-5

3-1,3-2,3-4,3-5

4-5,4-6,4-1,4-3

5-2,5-3,5-6,5-4

6-1,6-2,6-5,6-4

Unique:

1-2,1-3,1-4,1-6
2-3,2-5,2-6
3-4,3-5
4-5,4-6

Sums:
3,4,5,7
5,7,8
7,8
9,10

Unique:
3,4,5,7,8,9,10

So the answer is 7

Answer 16

Here's a net of a dice:
http://www.aspexsoftware.com/images/dice_cube_net.jpg

Answer 17

Factoid unrelated to this problem: The most likely sum tossed with a pair of standard number cubes (dice) is 7.

Answer 18

hmm... just curious... how long do you have on a question like this in your competition?

Answer 19

This would be a ciphering question: 2 minutes max.

Answer 20

high school?

Answer 21

Let's write the possible sums from 1 to whatever.
Can you can a sum of 1 adding the spots on two adjacent faces of the number cube?

Answer 22

No, there is not a face with zero on it. A sume of 1 is out.
Can you can a sum of 2?

Answer 23

i don't know if it is correct. Hope that someone can correct it for me...

Answer 24

Nah.. seems that i don't know the number arrangement in a dice :(

Answer 25

What exactly does a standard dice look like?

Answer 26

This one? http://www.aspexsoftware.com/images/dice_cube_net.jpg

Answer 27

Standard dice: http://homepage.ntlworld.com/dice-play/DiceStandard.htm

Answer 28

that means actually you can add 5and 6 which gives a 11...

Answer 29

the minimum sum of two faces of a die is 3 (1+2)
the maximum sum of two faces of a die is 11 (6+5)

the sum of two adjacent faces cant be 7(it is the sum of opposite faces)

so the possibilities are 3-4-5-6-8-9-10-11

so 8 possibilities

Answer 30

Can you not get a 6 and how do you get a 7? @ psuj

Answer 31

Seems like I'm not using a standard dice: http://www.aspexsoftware.com/images/dice_cube_net.jpg

Answer 32

Courtesy of hoblos -- This is it.

the minimum sum of two faces of a die is 3 (1+2)
the maximum sum of two faces of a die is 11 (6+5)

the sum of two adjacent faces cant be 7(it is the sum of opposite faces)

so the possibilities are 3-4-5-6-8-9-10-11

so 8 possibilities

Answer 33

your die is not a standard on @callisto

Answer 34

to become a standard one you must switch 4&5
now try

Answer 35

That was fun. Thanks, guys.

Answer 36

yeah.. thanks for the great question XD

Answer 37

yup... so i'm correcting it... not easy to get the answer :(

Answer 38

good job ;)