## asnaseer 3 years ago Reposting puzzle since no one has solved it yet: You are allowed to use any number of mathematical operators or functions (e.g. +, -, *, /, sin, cos, tan, factorial, sqrt, powers, etc) EXCEPT floor and ceiling functions. The only constants that can appear in the solution are two digits - both of which must be '2'. Use these rules to make the number 5.

1. FoolForMath

Can we use decimal point?

2. asnaseer

yes - looks like you may have found one of the solutions (I know 2 ways of doing this) :-)

3. FoolForMath

Well, don't you know I am the smart one? :P :D

4. asnaseer

of course I do :-)

5. FoolForMath

Anyways, I won't spoil the problem for others, but here is something related http://en.wikipedia.org/wiki/2_%2B_2_%3D_5

6. asnaseer

Wow - I guess you really do learn something new everyday - I was not aware of this - thx

7. FoolForMath

You are welcome :)

8. asnaseer

btw - there is a more /pure/ solution which does not involve using a decimal point

9. FoolForMath

I suppose we can't use variable substitution too, isn't ?

10. asnaseer

what do you mean @FoolForMath?

11. Zed

do the powers need to be 2 or anything?

12. asnaseer

remember the rules @Zed - you can ONLY have two constants in the resulting expressions and BOTH must be the digit '2'

13. Zed

ahh i see, read the question wrong

14. FoolForMath

Hm something like this: x=2; x^x + x^(x-x) = 5 :D wait that's with only one 2 :D

15. asnaseer

no sorry @FoolForMath - that is not allowed.

16. asnaseer

CLUE: the /purer/ solution involves right-angled triangles

17. FoolForMath

Hm then how about this one $$\csc^2(\cot^{-1}(2))$$ , Checking: http://www.wolframalpha.com/input/?i=Csc%5BArcCot%5B2%5D%5D%5E2

18. asnaseer

thats the one! - well done @FoolForMath can the others find the other solution?

19. FoolForMath

Thanks asnaseer :) Should I deleted it ?

20. asnaseer

5=cosec^2(arctan(2))

21. Zed

Well done FoolForMath

22. asnaseer

that is how I wrote it to avoid the "-1"

23. asnaseer

|dw:1325595329168:dw|

24. asnaseer

no need to delete your answer - lets see if anyone can find the other way of doing this

25. asnaseer

CLUE for other way: uses one decimal point, one squareroot and one power

26. FoolForMath

The other one is a bit hard in my opinion, I have seen this problem before sooo ;) anyways, the latex version of my solution $$\csc^2(\arccot(2))$$

27. asnaseer

$$cosec^2(arccot(2))$$

28. asnaseer

I wrote arctan above which was wrong.

29. FoolForMath

btw hey your earlier post is not correct 5 $$\neq$$cosec^2(arctan(2))

30. asnaseer

snap!

31. FoolForMath

wait, arccot is defined in latex no ?

32. FoolForMath

See: $\arccot \arctan$

33. asnaseer

hmmm...

34. Zed

okay i think this is right $\sqrt{0.2^{-2}}=5$

35. asnaseer

yup - you got it @Zed - well done!

36. FoolForMath

yep! you got that right :)

37. Zed

Yay! That was tricky :)

38. asnaseer

39. Zed

yeah i agree

40. asnaseer

so it /feels/ like cheating - but nevertheless - well done @Zed

41. FoolForMath

Hero wants hard, lets give him a bit harder :D I just found two other ways of getting the same result, could anybody wanna try ?

42. FoolForMath

Guys if you are trying, then please note it is not a good one and the second is ugly lol, and there is not much of useful maths we can learn from those two.

43. asnaseer

no - I was just waiting for @Hero to return to take up the challenge :-)

44. FoolForMath

lol :D asnaseer, wanna try something from my sleeve ? ;)

45. asnaseer

gulp! - I know your reputation @FoolForMath - but lets for it - you gonna post to the left?

46. asnaseer

*lets GO for it

47. FoolForMath

yeah sure :D

48. ixforrest

ummm this is kind o really easy.. at first I thought it was hard but i realized i was thinking too much.... 2^2 +2^3 = (12)^2 = 144 /2 = 72 /2 =36 /2 =18/2 =9 √9 = 3+2 = 5

49. ixforrest

no need for big guns this was basic problem solving skills

50. asnaseer

you didn't read the rules properly - the ONLY constants allowed are two digits - both of which must be the digit 2. e.g. 2^2+2^3 uses three 2's and a 3 - breaking the rules.

51. ixforrest

eh it was one of three or four answers ive got more. threre is also something interesting that happens between radians, but let me guess the implied conversion of a radian as 180 counts as a number other than 2 ? I still dont believe this requires higher level math I will stab at this later for now I have a date w/ Mathematica 8 and a vat of coffee. Thanks for clarifying !

52. asnaseer

:-D - enjoy the coffee!

53. ixforrest

always!