card game

[psi20]

I made up this new card game and the first version goes like this. You get a deck of cards and remove the jacks, queens, and kings. Now you have Aces and 2 to 10. Aces are worth 1 and the numbers are worth themselves. Shuffle the cards and pick 5 cards. Now with those five cards, make an equation. You can use + - x / ( ) powers and roots.

 

For example, if you picked up 9,5,1,2,7 you could make the equation (1*9+5)/2 = 7

 

If you picked up 9,5,6,3,3 you could make the equation 3*3^(6-5) = 9

 

The game gets harder--for me at least-- with the face cards in them. It's even harder (perhaps impossible) with some sets of 4 cards. But all the 5 card sets I've drawn can be made into equations.

 

This set of numbers gave me a hard time. The puzzle is to make an equation with 3,4,7,8,10.

[Guest pupil]

i have one for ya psi;

2 2 2

3 - 8 + 7 + 10=4

 

i wasnt sure how to type powers. I havent had a comp for very long, so i improvised.

[Guest pupil]

Crap. Didnt work. The 2's are to go above and to the right of the 3, 8, and 7.....LOL!

Any tips on typing the powers would be appreciated. Sorry for my noobness.

[psi20]

I don't know how to do powers either, except the old 3^2 - 8^2 + 7^2 + 10 = 4

 

But you can't do that because you didn't draw any twos. If you're going to use powers, both base and exponent must be drawn.

[Ducky Havok]

I got it.

 

The (cuberoot of 8)*7-4=10 (the cuberoot uses the 3)

 

edit: I added parenthases to lessen confusion

[ydoaPs]

that would need an ace:[imath]8^{\frac{1}{3}}*7-4=10[/imath], right?

[Ducky Havok]

no, I meant just the cube root of just 8 (2) and he said we could use roots

[ydoaPs]

i missed the part about roots

[psi20]

Yeah that works. I've been playing this game for a day, and I haven't come across a set which couldn't be done. (using 5 cards of ace through 10, I was stuck on sets of 4's) Is there a set which can't be put into an equation?

[psi20]

Now I'm having trouble with 2,2,5,5,12. Anyone got an equation for them?

[jcarlson]

Now I'm having trouble with 2,2,5,5,12. Anyone got an equation for them?

does sqrt require a 2 to use? or can we just sqrt something?

 

if it doesnt, then sqrt(5*5) * 2 + 2 = 12

[psi20]

Yeah, sqrt needs the extra 2.

[psi20]

I'm going to make a computer program to figure it out. Hope I'm done by tomorrow.

[psi20]

Oh, heh, didn't see this one.

 

12^(2-2) = 5/5