# 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.

Sibapriya DasguptaonParchi na! Please boley de!

Avijit BoseonHow about 2 to the power 4=16+3=19 ? Or we cant use power 4 ?

Rajib RoyonWhere did you get the 4 from?

Avijit BoseonReally ? I thought we can’t use squares

Avijit BoseonI got 21 a few minutes before. Let me remember

Rajib RoyonSorry, 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

Avijit BoseonOk you are right. Sorry. Let me try again

Bijetri Chakrabortyonuncle,my answer 2^5-13=19.is it right?

Bijetri Chakrabortyoncan I use 5 or not?

Rajib RoyonNo, only 1,2 and 3 (each only once and you have to use them)

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

Rajib RoyonYou can concatenate to form 21. But then what do you do with the 3?

Amitesh MukherjeeonOk. 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.

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

Rajib RoyonFunny, Ram but no π

Madhusudhan M. ReddyonCan you concatenate as 2(1)^3 to make 21?

Rajib RoyonNot 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.

Rajib RoyonBTW, 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.

Madhusudhan M. ReddyonYes, I was concatenating 2 and (1 to the power 3).

Sanjib BanerjeeonSame way you can get 19=1(3)^2

Amitesh Mukherjeeon19, 21 and three others. Kids are involved in this now. Will find out how they are doing once I retire from the court.

Madhusudhan M. Reddyon19 = sqrt((((3!)!)/2) + 1)

Madhusudhan M. Reddyon3!! = 720, 720/2 = 360, 360+1 = 361, and sqrt(361) = 19

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

Rajib RoyonAmitesh, 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

Rajib Royon20 I solved in the following way (3+1)/.2 I was a little proud of myself π

Rajib Royon17 is using my methodology above 2/.1 – 3

Chris KrameronI was stuck on 17, 19, 20, and 21. I guess now it’s full steam ahead to try and solve 21!

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

Rajib RoyonGo Chris! Go Madhusudhan!!

Chris KrameronLikely 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

Amitesh MukherjeeonOk 14 done. 17,19,20,21 still outstanding.

Amitesh MukherjeeonSaw Madhu’s answers. Awesome.

Amitesh MukherjeeonRajib Roy, I just saw your solution to 14. Ours was a little different (3/.2)-1.

Rajib RoyonI posted 17 and 20, Amitesh

Rajib RoyonAmitesh, and that is another great solution!!’

Amitesh MukherjeeonYou solved 20 in a similar fashion with a division by a decimal to get the multiplication effect.

Amitesh MukherjeeonYes I already saw all the other solutions Rajib Roy.

Rajib RoyonOur comments crossed the wires around the same time..,

Madhusudhan M. ReddyonThat’s interesting use of decimals for 17 and 20 which I was stuck on, besides 21.

Sanjib BanerjeeonHere is 21 ={ ((((2!)!)!) -1}*3 or 2!!!=8, 8 -1 = 7 , 7*3=21

Amitesh MukherjeeonHow are you getting 8 from 2!!! , Sanjib Banerjee ?

Bijetri Chakrabortyonuncle, we r trying only 19 & 21 but π

Rajib RoyonSanjib 2 factorial factorial factorial is still 2 not 8

Rajib RoyonBijetri, Madhusudhan uncle has solved 19. See above

Sreenivas MakalaonRajib Roy 12 in hexadecimal system is 18.(1*16+2*0) + 3 = 21. Is this allowed?

Rajib RoyonNo. But unique thought process..

Rajib RoyonAlso where did you get the 0 from? If we had a 0 would not the simple answer be 21 + 3*0?

Bijetri Chakrabortyonyes uncle,now i’m copying it . π

Madhusudhan M. Reddyonlshift(lshift(lshift(2))) + lshift(3) – 1 = 21, lol.