Puzzles with numbers and things

[davis_greatest]

Because everyone will see in your example that square root of -1 is wrong, but if you confuse them with i most people will be confused. :-)

I am not taking square root of -1... what I meant was

-1 = square root of [ (-1) squared ] = square root of [1] = 1

[elvaago]

Because everyone will see in your example that square root of -1 is wrong, but if you confuse them with i most people will be confused. :-)

[davis_greatest]

Why mess around with i? With that logic, you could just as well say:

-1 = square root of (-1) squared = square root of 1 = 1

[elvaago]

I'm not especially bright today, I'll take your word for it. I'll finish with the following gem, though:

Assuming that there is a number i for which goes i^2 = -1 you can deduce the following:

-1 = i^2 = i * i = square root of -1 * square root of -1 = square root of (-1 * -1) = square root of (-1^2) = square root of 1 = 1

Therefore, -1 = 1

[davis_greatest]

Are you satisfied with the question and answer now, elvaago and rambon?

[snookersfun]

Haha, of course not. Why would I have had a range otherwise?
got to the 10 in about the same way (only possibility to get same # of digits), after that figures that the number has to be around 9.9 (bit smaller in fact), therefore 2nd answer 98 and third 970 (as really tiny numbers are added to those, they couldn't have been the next highest numbers)

[davis_greatest]

I feel smoking heads... and I don't feel so silly anymore

Hehe. Did you solve it the same way?

[snookersfun]

I feel smoking heads... and I don't feel so silly anymore

[davis_greatest]

Why are you subtracting 2 and 30 from respectively 100 and 1000? I don't see anywhere in your problem that you have to deduct anything from anything.

What we know is that Charlie tells davis_greatest a Special Number S, which I add to its reciprocal to get
S + 1/S. Call this answer "Davis".

Charlie tells Gordon the square of the special number S^2, which Gordon adds to its reciprocal to get
S^2 + 1/S^2. Call this answer "Gordon".

Charlie tells Oliver the cube of the special number S^3, which Oliver adds to its reciprocal to get
S^3 + 1/S^3. Call this answer "Oliver".

With some algebra (shown above) - regardless of the value of the special number S - you get:

Gordon = Davis^2 – 2

and

Oliver = Davis^3 - 3 x Davis.

That's why you don't need a calculator - because at the end all you need to calculate is
10 x 10 x 10 - 3 x 10 = 1000 - 30 = 970.

[davis_greatest]

I think he means that S + 1/S = 10, where S is not 10, but more something like, 9.89.

Precisely. You don't have to know the Special Number S to solve the problem. But in fact S + 1/S = 10, so S could be either about 9.899 or about 0.101.

[elvaago]

I think he means that S + 1/S = 10, where S is not 10, but more something like, 9.89.

[rambon]

You've lost me for the first time I think.

If you add the reciprocal of 10 (1/10) to 10, you get 10.1 don't you? Why is that a whole number. I've just spent eight hours on a plane, so I admit that jetlag might have played a role in this.....

[elvaago]

Why are you subtracting 2 and 30 from respectively 100 and 1000? I don't see anywhere in your problem that you have to deduct anything from anything.

[davis_greatest]

snookersfun extends her lead

hopefully 970, after a bit more thought.

970 is the correct answer. Well done!

Let S = the Special Number

and davis_greatest’s answer be Davis = S + 1/S
and Gordon’s answer be Gordon = S^2 + 1/S^2
and Oliver’s answer be Oliver = S^3 + 1/S^3

Then Davis^2 = (S + 1/S)^2 = S^2 + 1/S^2 + 2 = Gordon + 2
So Gordon = Davis^2 – 2

Gordon has the same number of digits as Davis.
Davis has more than one digit, so Davis >=10
If Davis = 10, the Gordon = 10^2 – 2 = 100 – 2 =98 which has the same number of digits as Davis.
If Davis>=11, then Gordon = Davis^2 – 2 has more digits than Davis.

So Davis = 10.

Once we know this, there is more than one way of getting Oliver’s answer. One way is to note that
Davis^3 = (S + 1/S)^3 = S^3 + 1/S^3 + 3S + 3/S = Oliver + 3 Davis

So Oliver = Davis^3 – 3 Davis = 10^3 – 3x10 = 1000 – 30 = 970



SO HERE IS THE SCOREBOARD AFTER ROUND 31

snookersfun……………………….…..15
Vidas……………………………………….8½
robert602…………………………………5
abextra……………………………..…...4½
davis_greatest…………………..……3

(some rounds may be worth more than one point)
(especially ones won by davis_greatest)

[elvaago]

Thank you.