matchstick equations

Here are a few samples of matchstick equation problems I designed for my math class. The rules of the game are: 1) You must use all the matchsticks 2) You can't break, bend, etc. any matchstick 3) Allowed symbols are: 0 through 9, +, -, /, X and = 4) Using not equals (a line through a =) is not allowed! 5) +, = and X are both 2 matchsticks each (all the sticks are the same size but I can't show this just using text)

Here is a simple example. Move 1 matchstick and make the equation true: _ _ _ _ + _ = _ _ _ _ The only solution is: _ _ _ _ + _ = _ <

SPOILER (Partial)

_ _ _ _ _ = _ _ _ _ _ _ = _ _ _ _ _ _ _ + _ = _ _ _ _ _ _ _ _ _ + _ = _ _ _ _ _ _ _ _ _ = _ _ _ _ _ _ _ _ + = _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ = _ _ _

Ilan Mayer heeft geschreven in bericht ...

v

v

v

v

_ _ _ _ _ _ = _ _ _

Good work, Oops, turns out that there are TWO solutions to: So there is still one solution missing. (I missed Ilan Mayer's solution, thanks)

There is still 1 missing solution to:

There is still 1 missing solution to:

This is a creative solution! What I have in mind for all the problems is that all numbers and symbols should be the correct size. I should of put this in my original rules! So writing 11 as you did would be out, also writing: _ _

for 10 would also be out. I can give elliptical hints if anyone wants. Have fun Alan

PS: wizengy, I am impressed with you figuring out the upside-down trick since none of my students figured this one out

SPOILERS

5

4

3

2

1

0

thanks)

Probably another different solution. Upside down we have _ _ _ _ _ _ _ _ = _ + _ _ _ _ _ _

_ _ _ _ _ _ _ / _ = + _ _ _ _ _ _

_ _ _ _ _ = _ _ _

_ _ _ _ = _ = _ _ _ _

Nice work Justin As you observe this solution is different from the one I have. But you aced the others. Still one more!

Alan PS: This problem has given me a headache. I had a slightly different version that ended up having so many solutions that I abandoned it in favor of this one (which as you can see I didn't test thoroughly!). So the race is on. Can we find even more solutions than the one

Another two solutions follow

Another right side up solution: _ _ _ _ _ _ - _ = _ - _ - _ _ _ _ _ _

Another upside down solution: _ _ _ _ _ _ _ / _ = _ - _ _ _ _ _ _

Hopefully one of the above matches your intended solution. I'm tempted to write a computer program to exhaustively find solutions, but that would take the fun out of solving them manually.

*Move 2 matchsticks and make the equation true. * * _ _ _ _ _ * _ / _ = _ _ _ * _ _ _ _ _

SPOILER

_ _ _ _ _ _ _ / _ = _ _ _ _ _ _ _ _

I think that -2^8=-256 (remember (-2)^8 = 256) so close but not quite it. Of course this is a case that I didn't think about! And I should in the future take this possibility into account. You can make the above concept work, can you find out how? Argh, this problem is giving me a headache! So can anyone find a solution that doesn't involve ^? Will I be able to hold my head up high as a puzzlemister and get this one right? Happy hunting

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