## asnaseer Group Title 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. 2 years ago 2 years ago

1. FoolForMath Group Title

Can we use decimal point?

2. asnaseer Group Title

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

3. FoolForMath Group Title

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

4. asnaseer Group Title

of course I do :-)

5. FoolForMath Group Title

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 Group Title

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

7. FoolForMath Group Title

You are welcome :)

8. asnaseer Group Title

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

9. FoolForMath Group Title

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

10. asnaseer Group Title

what do you mean @FoolForMath?

11. Zed Group Title

do the powers need to be 2 or anything?

12. asnaseer Group Title

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

13. Zed Group Title

ahh i see, read the question wrong

14. FoolForMath Group Title

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

15. asnaseer Group Title

no sorry @FoolForMath - that is not allowed.

16. asnaseer Group Title

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

17. FoolForMath Group Title

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 Group Title

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

19. FoolForMath Group Title

Thanks asnaseer :) Should I deleted it ?

20. asnaseer Group Title

5=cosec^2(arctan(2))

21. Zed Group Title

Well done FoolForMath

22. asnaseer Group Title

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

23. asnaseer Group Title

|dw:1325595329168:dw|

24. asnaseer Group Title

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

25. asnaseer Group Title

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

26. FoolForMath Group Title

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 Group Title

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

28. asnaseer Group Title

I wrote arctan above which was wrong.

29. FoolForMath Group Title

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

30. asnaseer Group Title

snap!

31. FoolForMath Group Title

wait, arccot is defined in latex no ?

32. FoolForMath Group Title

See: $\arccot \arctan$

33. asnaseer Group Title

hmmm...

34. Zed Group Title

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

35. asnaseer Group Title

yup - you got it @Zed - well done!

36. FoolForMath Group Title

yep! you got that right :)

37. Zed Group Title

Yay! That was tricky :)

38. asnaseer Group Title

39. Zed Group Title

yeah i agree

40. asnaseer Group Title

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

41. FoolForMath Group Title

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 Group Title

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 Group Title

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

44. FoolForMath Group Title

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

45. asnaseer Group Title

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

46. asnaseer Group Title

*lets GO for it

47. FoolForMath Group Title

yeah sure :D

48. ixforrest Group Title

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 Group Title

no need for big guns this was basic problem solving skills

50. asnaseer Group Title

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 Group Title

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 Group Title

:-D - enjoy the coffee!

53. ixforrest Group Title

always!