There is so much great stuff out there, I just need more time to explore it. ]]>

When I do the four fours with students, I allow a few other operations. We can use two fours to write forty-four, or use a decimal point to write “4.4” or “.4”. If we’re allowed to do that, we could write “(4/.4)+(4/4)” and “(4-.4)/.4 + 4”. I allow the square root as an operation, too, and that comes in handy sometimes: “44/4 + sqrt(4)”. Maybe some new operations will spark your students to find new solutions!

And, in a bit of shameless self-promotion, I’ll mention that Challenge 05 over at collaborativemathematics.org has a similar feel to the four fours, in the sense that the goal is to build an expression out of some given building blocks. If your students liked the four fours, they might like “pieces of eight” ! ðŸ™‚

]]>I started toying around with possibilities for 11 and 13. We could brute force attack the problem to find all possible outcomes. We would need to define which operations are permissible (+, -, x, / ) as well as whether or not we treat the 4’s as distinct, e.g., if the 4’s were all different colors. We also need to be explicit on commutativity, associativity, etc.

I wrote up a shotgun expression assuming four operations and associativity. We could account for commutativity by multiplying by a factor or two.

Sum (k = 0 to k = 4) (4 choose k) * 4^3 where k = the number of 4’s associated together

Again, I know this isn’t very rigorous and doesn’t do ALL the counting, but it’s a start!

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