## This Was Probably a Bad Idea

*December 12, 2007 at 9:17 am* *
1 comment *

You are about to witness the lamest blog post ever crafted by human hands. Those with a shred of respectability or coolness left should turn away now.

You have been warned.

I was on the XKDC forums and came across the following math puzzle:

Suppose that you have a standard scientific calculator. We can press any combination of keys, but the only digit that you’re allowed to touch is 2, and you’re only allowed to hit it 3 times. For instance we could press 2 – 2 / 2 = to get a 1.

The puzzle, figure out how to produce every number from 1 to 12.

Now, because (as we’ve established) I’m a huge geek, I instantly attempted to solve this. It took a few minutes, but I got them all worked out.

So, as a challenge to anyone who reads this: come up with answers and post them as comments. I’ll do the same with mine, but don’t read them until you’ve had a go at it. Each problem should have multiple solutions, and I’m interested in seeing what other people come up with. It’ll be all kinds of fun!

Assuming you think math is fun.

If anyone wanted to kill me now, you could not be blamed.

Entry filed under: Uncategorized. Tags: math.

1.elminko | December 15, 2008 at 11:33 pmOkay, here’s what I got. Explanations will follow.

1 = 2 – (2 / 2)

2 = 2

3 = 2 + (2 / 2)

4 = 2squared

5 = 2squared + (2 / 2)

6 = 2 + 2 + 2

7 = [(2squared)squared – 2] / 2

8 = 2squared x 2

9 = [(2squared)squared + 2] / 2

10 = 2squared x 2 + 2

11 = 22 / 2

12 = (2squared)squared – 2 – 2

These problems are made easy when you realize scientific calculators always have a “squared” button, giving you a way to increase the value without wasting your three alloted “2’s”

For several of these, I arrived at the answer by considering the wording of the problem. When the problem says “you’re only allowed to hit (2) three times” most readers assume they HAVE to use 2 three times; however, this is not the case, resulting in simple solutions to ‘2’, ‘4’ and ‘8’.

In addition, the wording implies that you can only use the number ‘2’; however, on closer inspection, it becomes clear you can use any number so long as it consists only of 2’s, making for an elegant solution to 11.

My answers to 7, 9, and 12 are a little cumbersome, so I’ll solve them here. For 7 the answer is:

[(2squared)squared – 2] / 2

=(4squared – 2) /2

=(16 – 2) / 2

=14 / 2

=7

For 9, the solution is:

[(2squared)squared + 2] / 2

= (4squared + 2) / 2

= (16 + 2) / 2

= 18 / 2

= 9

The answer to 12 is also a little awkward, so:

(2squared)squared – 2 – 2

=4squared – 2 – 2

=16 – 2 – 2

=12

The real challenge here is to come up with solutions that are simpler than the ones I used. Anyone actually going to do this?