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.
Parchi na! Please boley de!
How about 2 to the power 4=16+3=19 ? Or we cant use power 4 ?
Where did you get the 4 from?
Really ? I thought we can’t use squares
I got 21 a few minutes before. Let me remember
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
Ok you are right. Sorry. Let me try again
uncle,my answer 2^5-13=19.is it right?
can I use 5 or not?
No, only 1,2 and 3 (each only once and you have to use them)
Placing 1 next to 2 to make 21 – is that allowed ? Or you must have some kind of mathematical operation to derive the number ?
You can concatenate to form 21. But then what do you do with the 3?
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.
Rajib- would using different bases work? like 32 in base 16 is 20, add the 1 in base 10 = 21; after all #lifeisallaboutapplesandoranges
Funny, Ram but no 🙂
Can you concatenate as 2(1)^3 to make 21?
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.
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.
Yes, I was concatenating 2 and (1 to the power 3).
Same way you can get 19=1(3)^2
19, 21 and three others. Kids are involved in this now. Will find out how they are doing once I retire from the court.
19 = sqrt((((3!)!)/2) + 1)
3!! = 720, 720/2 = 360, 360+1 = 361, and sqrt(361) = 19
Outstanding Madhusudhan!! Hats off!!! Only you can solve 21 for the rest of us. Again, mindblowing!!!
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
20 I solved in the following way (3+1)/.2 I was a little proud of myself 🙂
17 is using my methodology above 2/.1 – 3
I was stuck on 17, 19, 20, and 21. I guess now it’s full steam ahead to try and solve 21!
Sanjib, that is illegal use of concatenation. Expressions cannot be concatenated in math. Digits can be.
Go Chris! Go Madhusudhan!!
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
Ok 14 done. 17,19,20,21 still outstanding.
Saw Madhu’s answers. Awesome.
Rajib Roy, I just saw your solution to 14. Ours was a little different (3/.2)-1.
I posted 17 and 20, Amitesh
Amitesh, and that is another great solution!!’
You solved 20 in a similar fashion with a division by a decimal to get the multiplication effect.
Yes I already saw all the other solutions Rajib Roy.
Our comments crossed the wires around the same time..,
That’s interesting use of decimals for 17 and 20 which I was stuck on, besides 21.
Here is 21 ={ ((((2!)!)!) -1}*3 or 2!!!=8, 8 -1 = 7 , 7*3=21
How are you getting 8 from 2!!! , Sanjib Banerjee ?
uncle, we r trying only 19 & 21 but 🙁
Sanjib 2 factorial factorial factorial is still 2 not 8
Bijetri, Madhusudhan uncle has solved 19. See above
Rajib Roy 12 in hexadecimal system is 18.(1*16+2*0) + 3 = 21. Is this allowed?
No. But unique thought process..
Also where did you get the 0 from? If we had a 0 would not the simple answer be 21 + 3*0?
yes uncle,now i’m copying it . 🙂
lshift(lshift(lshift(2))) + lshift(3) – 1 = 21, lol.