Chef's Quick Brain Teaser, revisited

[Bagpuss]

Well to my simple mind, if the formula above was correct then if X1=1 X0 = 0

0*1 = ?

[DaveB]

0*1 = ?

Told you I was simple

and apparently unable to read ()'s corectly.....

[Bagpuss]

Told you I was simple

and apparently unable to read ()'s corectly.....

BODMAS mate BODMAS

Where's CUK's self proclaimed maths whiz?

He reads maths books as a hobby so maybe he should be setting the questions

[ASB]

Another HUGE hint.

What number came BEFORE in the series 1, 2, 6, 42, 1806, ...

I.e., what comes before the '1'?

If you take the obvious solution for the series then yes - and that would then define the series as one of the possible solutions. See OwlHoots link for other solutions that are valid with that sequence.

[SallyAnne]

Is there a "hanging oneself" smilie available?


I'll settle for this

[expat]

All I can see in question 1 is

x = x * (x + 1);

I thought it was

x = (x * x) + x

They are algebraically identical. However Churchill's shows the rule that is probably in mind to generate the series.

x(n+1) = xn * (xn + 1)

[EternalOptimist]

They are algebraically identical. However Churchill's shows the rule that is probably in mind to generate the series.

x(n+1) = xn * (xn + 1)

Ah , but now observe


n = x * (x+1)
n = (x*x) + x

therefore

x * (x+1) = (x*x) +x

therefore

x = sqrt((x*(x+1)-x)


I refer to this as 'The Golden Rivet' (Which, colloquially, is an eight incher)

[TimberWolf]

If x1 = x0 * (x0 + 1)

then x0 * (x0 + 1) = x1

Where x1 = 1 calculate x0 and put it in the series.

[1] x1 = (1 + x0)x0, so x0 = ( -1+-sqrt(1-4x1) ) / 2
[2] x1 = (1 + x0)/x0, so x0 = 1/(x1-1)

[Bagpuss]

They are algebraically identical. However Churchill's shows the rule that is probably in mind to generate the series.

x(n+1) = xn * (xn + 1)

which is the same as

it should be X(n)=X(n-1)*[X(n-1) +1]

[expat]

<expat's>
which is the same as
<Bagbuss's earlier>

I agree a million percent.




x(n+1) = xn * (xn + 1)

so xn**2 + xn - x(n+1) = 0

when x(n+1) = 1,
xn = [ -1 +/- sqrt(1 + 4) ] /2
positive root = [ -1 + sqrt(5) ] /2 = 0.618 etc

I wasn't going to bother going through with it: the maths is only school-level but the notation is painfully ponderous in plain text.