- #1
Mingy Jongo
- 5
- 0
Suppose I am playing a game where I roll some dice, and must use only combinations of elementary operations (addition, subtraction, multiplication, or division) to make an equation using each number rolled exactly once.
For example, if I roll four six-sided dice, and get this:
2, 3, 3, 4
A possible solution is:
3-2=4-3
Another one is:
(3+3)-2=4
Now, I'm fairly certain that for up to five six-sided dice, not all combinations can be made into valid equations. Here are some examples:
2 dice: Everything except doubles
3 dice: Triples greater than 1s; two 1s and a 3, 4, 5, or 6
4 dice: Three 1s and a 4, 5, or 6
5 dice: Four 1s and a 5 or 6
My question is, are there any combinations that cannot be made into valid equations for six six-sided dice? Five ones and a six works here: (1+1)*(1+1+1)=6
If so, can someone give me an example of such a combination, and more interestingly, the minimum number of six-sided dice needed to guarantee a valid equation for any possible roll, if there indeed exists a minimum?
For example, if I roll four six-sided dice, and get this:
2, 3, 3, 4
A possible solution is:
3-2=4-3
Another one is:
(3+3)-2=4
Now, I'm fairly certain that for up to five six-sided dice, not all combinations can be made into valid equations. Here are some examples:
2 dice: Everything except doubles
3 dice: Triples greater than 1s; two 1s and a 3, 4, 5, or 6
4 dice: Three 1s and a 4, 5, or 6
5 dice: Four 1s and a 5 or 6
My question is, are there any combinations that cannot be made into valid equations for six six-sided dice? Five ones and a six works here: (1+1)*(1+1+1)=6
If so, can someone give me an example of such a combination, and more interestingly, the minimum number of six-sided dice needed to guarantee a valid equation for any possible roll, if there indeed exists a minimum?