mathematical problem

[BabsG]

Using any acceptable mathematical notation how can you express the number 5 by using exactly two 2s? Any ideas anyone, please?

[Russyfoot]

Is this a trick question ?? 2+2+1=5 using exactly two 2's.

[BabsG]

That's the way my mind works too. But, knowing the devious way in which this particular quiz setter works, the answer will probably have only two 2s and a mathematical sign. My knowledge of maths is zilch so it's all a mystery to me.

[DOB]

Hi BabsG. You don't say if you can use letters or not but here goes anyway. This is kind of a long shot but there is a mathematical function called a LOG or LN if you use the standard. I'm not really sure what it stands for or anything, but the standard used is 2.7182818 and is represented by the letter "e". Anyway the symbol/formala LN(e)=1 so if you write 2+2+LN(e) then that equals 5. Hope this helps. Please reply whether this is correct or not 'cos it's killing me if it's wrong

[BabsG]

Thanks DOB. I won't know if you are right or wrong till the end of Aug when the answers come out. I will let you know then.

[wiseman3175]

Why not try 2 squared plus 2 raised to the power of zero? Or would the squared count as one of the two's?

[Brugel]

DOB's answer seems fine except that if you use ln e then it's possible to express 5 using only one 2 (for it can be written as 2 + ln e + ln e + ln e. In fact, it can be written without using a 2 at all). There are also various other ways of making up the extra 1. For example, (sin x)squared + (cos x)squared + 2 x 2 = 5. Or, negative e to the power of i times pi + 2 x 2 = 5. Finally, how about [e squared] - 2 = 5 where the brackets [ ] indicate that you take the greatest possible integer below e squared (this is standard mathematical notation and perfectly acceptable).

[bernardo]

I have thougth of a way of doing it using mathematical symbols with oly two 2s but without using any other numbers or letters like ln or log or e or pi.

the square root of (.2 [to the power of] -2)

[bernardo]

misprint!

only, not oly. btw The typeface is too small and it may not be obvious that there is a decimal point before the first 2.

[DOB]

That's pretty good Bernardo. I was thinking about the problem in work today and as Brugel says, there are countless ways to make the extra 1 (x/x is prob the simplest). The only thing possibly wrong (and I'm nitpicking) is that the square root sign technically contains a figure 2 just above the v section of the sign so hopefully that "2" doesn't count as one of the twos used.

[BabsG]

I'm really impressed that all you guys seem to know what you are talking about. Education is not dead after all. Thanks everyone.