## Can Two 2’s Produce 5?

Using only two 2’s and any mathematical operations, functions and symbols that you want (and I mean ANY!), try to make two 2’s equal to 5. Trust me, this problem is harder than it looks as you would find out if you choose to solve this problem. So, if you really want a difficult challenge, then try to solve this first before looking at the solution.

## Solution

When a friend of mine gave this problem to me , I thought that it’s not even that challenging. I was very surprised at the level of difficulty of this deceptively simple-looking problem. Through several trials and errors and probably dumb luck, I eventually solved it but I felt very dizzy afterwards.

Now, here’s the solution,

$\sqrt{.2^{-2}}$, which is equal to $\sqrt{25}=5$

Note that $.2^{-2}=\frac{1}{(.2)^2}=\frac{1}{.004}=25$

As you can see, the solution involved a decimal, a square root, an exponent and a negative number! If you also found this solution by yourself, then I’d like to congratulate you.

In hindsight, it’s pretty easy to find another solution. Admittedly, though, it’s almost the same as the first solution:

$(\sqrt{.2})^{-2}=\frac{1}{\sqrt{.2^{2}}}=\frac{1}{.2}=5$

My name Edmark M. Law. I work as a freelance writer, mainly writing about science and mathematics. I am an ardent hobbyist. I like to read, solve puzzles, play chess, make origami and play basketball. In addition, I dabble in magic, particularly card magic and other sleight-of-hand type magic. I live in Hong Kong. I blog at learnfunfacts.com. You can find me on Twitter @EdmarkMLaw and Facebook. My email is learnfunfacts@gmail.com
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### 10 Responses to Can Two 2’s Produce 5?

1. From E. E. Cummings’ prelude to his book, entitled “is 5″ :

On the assumption that my technique is either complicated or original or both, the publishers have politely requested me to write an introduction to this book.
At least my theory of technique, if I have one, is very far from original; nor is it complicated.
I can express it in fifteen words, by quoting The Eternal Question And Immortal Answer of burlesk, viz.”Would you hit a woman with a child? – No, I’d hit her with a brick.” Like the burlesk comedian,
I am abnormally fond of that precision which creates movement.
If a poet is anybody, he is somebody to whom things made matter very little–somebody who
is obsessed by Making. Like all obsessions, the Making obsession has disadvantages; for instance, my only interest in making money would be to make it. Fortunately, however, I should prefer to make almost anything else, including locomotives and roses.It is with roses and locomotives (not to mention acrobats Spring electricity Coney Island the 4th of July the eyes of mice and Niagara Falls) that my
“poems” are competing.
They are also competing with each other, with elephants, and with El Greco.
Ineluctable preoccupation with The Verb gives a poet one priceless advantage: whereas
nonmakers must content themselves with the merely undeniable fact that two times two is four, he rejoices in a purely irresistible truth (to be found, in abbreviated costume, upon the title page of the present volume).

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2. Excellent problem. I took a long while, but never quite got there!

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3. Bunk Strutts says:

Assume that we’re talking about parents and offspring. The first couple (2a) has twins, the second couple (2b) has triplets. Combining the number of offspring between them, 2a + 2b = 5.

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• Bunk Strutts says:

I see that html doesn’t fly here. The letters should be subscripts. 😀

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• Yes, it doesn’t. Only LaTeX works here with restrictions.

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• Bunk Strutts says:

BTW, 2 x 1 = 10 if we’re talking about a pair of rabbits mating once.

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• I heard that during the 19th century, three wild rabbits in Australia became millions in just a few years 🙂

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4. I like this one. It makes sense.

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