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.(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Making equations with six six-sided dice

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