22 May 2015

Puzzle time in India !

Today was the last evening in Kalyani this trip. Like everyday, after dinner, we all went for a walk. “All” means the nephews, niece, my brother, sister, brother in law and of course myself. We, the adults, chat about a lot of things and I usually give the kids some math or logic puzzle to keep them busy.

Today started as an innocuous puzzle. But the adults joined in too. As a result, we amped up the difficulty of the puzzle. We have not been able to solve it fully. Maybe you can…

The puzzle is simple – using just the digits 1, 2 and 3 (each only once) derive all numbers from 0 to 25. You can use any of the following mathematical symbols any number of times : plus, minus, multiplied by, divided by, factorial, square root of, decimal point and parentheses (+ – * / ! Sqrt . and () ). For the programming types, ++ and — are not mathematical symbols.

E.g you can get 7 by 21/3 or 3*2+1 etc etc

We got everything other than 19 and 21. Still stuck.

Care to give it a try?

I am going to sleep now – will check tomorrow morning. Feel free to answer in Comments section.

Posted May 22, 2015 by Rajib Roy in category "Puzzles", "Vacations


  1. By Rajib Roy on

    Sorry, I read it too quickly. You can use “to the power” (there is no mathematical operator required). But where are you getting 4 from? It is 1 2 and 3

  2. By Amitesh Mukherjee on

    Placing 1 next to 2 to make 21 – is that allowed ? Or you must have some kind of mathematical operation to derive the number ?

  3. By Amitesh Mukherjee on

    Ok. I didn’t realize you have to use all three numbers. I read it as ” you can’t use anything but 1,2,3″. Search for answers continue.

  4. By Ram Narayanan on

    Rajib- would using different bases work? like 32 in base 16 is 20, add the 1 in base 10 = 21; after all #lifeisallaboutapplesandoranges

  5. By Rajib Roy on

    Not sure how that expression evaluates – it would be 2 right? (the exponent would be done first – so 1 to the power 3 is 1. and then multiply by 2). Are you concatenating 2 and (1 to the power 3). That will not work. You can concatenate digits – concatenating expressions wont make sense.

  6. By Rajib Roy on

    BTW, have you guys gotten all the number from 1 thru 25 and are stuck on 19 and 21 like us? Or did you not try those numbers at all? Madhusudhan, Amitesh, Bijetri, Chris, Avijit, Sibapriya.

  7. By Rajib Roy on

    Outstanding Madhusudhan!! Hats off!!! Only you can solve 21 for the rest of us. Again, mindblowing!!!

  8. By Rajib Roy on

    Amitesh, we were all stuck on 14 for a while. The youngest nephew solved it : 3 factorial is 6 plus 1 is 7 multiplied by 2 is 14

  9. By Rajib Roy on

    Sanjib, that is illegal use of concatenation. Expressions cannot be concatenated in math. Digits can be.

  10. By Chris Kramer on

    Likely not a symbol and thus not allowed but I should get style points. F( (2^3) * 1) where F is Fibonacci. So the 8th digit in the Fibonacci sequence – F(8) = 21


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