In honor of the fact that I turn 24 today, I’m posting a puzzle that Deb posed to me, Anand, Breath, and Resa at a dimsum outing in San Francisco back in June. She really should have known better than to do this at a table of MIT alums, as the rest of the meal was very quiet while we all stared into space trying to figure it out.

Using only basic arithmetic operations (+,-,*,\), represent the number 24 using two 10s, a 2, and a 4. For example, representing 26 can be done as “10+10+2+4” or “2*10+10-4” (and if I was cool, like Anand, I’d write those equations in a LaTeX font — but obviously I’m not).

After two days of none of us getting it, Breath actually wrote a python script to solve this. In the meantime, my dad gave it to a guy at his work who solved it using his own brain power in 15 minutes. And how will you solve it? (The aforementioned people are not allowed to answer.)

And for a more historical look on this day that is sure to be a holiday at some point, check out last year’s entry.

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Is it cheating to just say 24 + 10 – 10?

Yep, that’s cheating. The 2 and 4 are used as distinct numbers.

happy birfday!!!!!!!!1

thanks for the memories.

-(4-10)*2 + 10 = 24

🙂

Am I right??

Oh no! I can’t do arithmetic anymore!! That equaled 22, I’ll try again…

I GOT IT!!!!

10*((4/10)+2) = 24

WOOT!!!

Laura wins… although, to be fair, Amittai also solved it, but sent me the solution via e-mail:

> $$ (2 + \frac{4}{10}) \cdot 10 $$

>

> they say one thinks best when one is thinking

> about something else: 10 minutes, most of which

> were spent watching harvey eat the lamp post

> over and over and over 🙂

>

> ~amittai

I got it in about twenty seconds. But I’ve seen this type of problem before. (Any time a 24 puzzle seems impossible but somebody assures you it’s doable, and it has a repeated number, you probably want to use the divide-add-multiply trick.)

See Dan’s comment. I first saw this years ago; it was with 3, 3, 7, 7, but it’s the same idea.