## asnaseer 3 years ago Puzzle time: You are allowed to use any number of mathematical operators or functions (e.g. +, -, *, /, sin, cos, tan, factorial, sqrt, etc) but only two constants both of which must be the number 2.

1. asnaseer

Use these rules to produce the number 5.

2. karatechopper

what r sin cos tan and factorial?

3. asnaseer

they are trigometry functions

4. asnaseer

*trigonometry

5. karatechopper

i dont knw em..

6. karatechopper

do we need to know then for this?

7. asnaseer

I know of two ways of solving this - one requires the use of trig functions but the other one does not...

8. karatechopper

3+2

9. asnaseer

you are not allowed to use the number 3. the only "number" you can use are 2 and 2 - i.e. two 2's

10. karatechopper

o..

11. moneybird

Can you use floor and ceiling functions?

12. asnaseer

Unfortunately not...

13. karatechopper

do u have to use both of the 2s?

14. asnaseer

yes - the expression you end up with must have exactly two 2's within it

15. karatechopper

ok

16. karatechopper

haha thts what ijust typed in my calc

17. karatechopper

but its not 5

18. asnaseer

@moneybird - that works out to be 2 doesn't it?

19. moneybird

i though it needs to be equal to 2 my bad

20. asnaseer

:-)

21. karatechopper

haha yea

22. karatechopper

can there be more 2s?

23. asnaseer

trying to use floor and ceiling functions was a clever thought though @moneybird

24. karatechopper

what r floor and ceiling functions?

25. asnaseer

floor(1.5678)=1 ceiling(1.5678)=2

26. asnaseer

floor basically says "drop the decimal part"

27. asnaseer

ceiling says "round down to integer"

28. asnaseer

*up

29. karatechopper

o

30. karatechopper

can we more than just two 2s?

31. asnaseer

nope

32. karatechopper

hmm

33. asnaseer

both answers that I have are /fairly/ simple - so no magical complicated functions are needed

34. karatechopper

o..

35. karatechopper

is one of them with no trignometric functions in it?

36. asnaseer

correct

37. karatechopper

ok..so it has like somple ones tht a third grader is familiar with?

38. asnaseer

yup

39. karatechopper

like +,-,/,*

40. asnaseer

a bit more than just those...

41. karatechopper

factorial and sqrt?

42. asnaseer

it has sqrt and powers in it...

43. karatechopper

o..

44. karatechopper

if i use 2 as a power, does it still count as one of the 2s?

45. asnaseer

yes

46. asnaseer

but the purer answer uses only trig functions

47. karatechopper

argh..

48. asnaseer

who said this was going to be easy? ;-)

49. karatechopper

not me!

50. asnaseer

:-)

51. karatechopper

hmmm i need clues...

52. asnaseer

I gave you a clue already: it has sqrt and powers in it...

53. karatechopper

but u can have only two 2s! and if i say 2 to the power of 2 then my 2s r used!!!!

54. asnaseer

correct - so think of other ways of using sqrt and powers - and remember "power" does not mean it has to be to the power to "2". as long as the only digits that appear in the answer are two 2's - then the solution is valid.

55. karatechopper

so u mean they can be to the power of any number?

56. asnaseer

if I say anymore I will give the answer away :-)

57. karatechopper

hmmmmmmmm