- animeshsaxena
**Posts:**520**Joined:**

From the diagram I guess it's an incircle for the smaller triangle.The angle bisectors will hit the incenter, so first I need to find the two angles.One of them is obviously 45degree. Other one after some trig...can be found to be 63.43(approx)Tan[45/2] = r/xTan[63/2] = r/[a-x]a-x + x = r/tan[45/2] + r/tan[63/2]I had drawn a perpendicular from circle centre to opposite side...so r = tan[45/2]tan[63/2]/(1+tan[45/2]tan[63/2])

a*2/(sqrt(5)+sqrt(8)+sqrt(9)) or a*(1+sqrt(2)+sqrt(5)-sqrt(10))/6any other interesting form?----- ----- ----- ----- -----hmm... scooped:(

Last edited by wileysw on May 7th, 2011, 10:00 pm, edited 1 time in total.

- animeshsaxena
**Posts:**520**Joined:**

Made a very very silly mistaker = tan[45/2]tan[63/2]/(1+tan[45/2]tan[63/2])should have beenr = tan[45/2]tan[63.43/2]/(tan 45/2 + tan [63.43/2]) = 0.248instead of writing 1 + in the denominator....must be slope formula swirling in my head....Had verified the answer...but instead of typing it...wrote the silly formula I agree damn stupid Definitely 0 points for this!

- Traden4Alpha
**Posts:**23951**Joined:**

Hmm... Technically, the problem statement is ill-formed. What is the height of the outer rectangle?

- Traden4Alpha
**Posts:**23951**Joined:**

No. This problem is a 3-D variant on a knights tour problem in which each move is down one unit in two of the dimensions and up two units in one dimension.This movement pattern means that the differences in the population values remain constant modulo 3 after any change. Achieving a monochromatic population requires a modulo 3 difference of 0 between two elements in the initial condition and the given initial condition of [20,18,16] has modulo 3 differences of 2.

Last edited by Traden4Alpha on May 9th, 2011, 10:00 pm, edited 1 time in total.

- katastrofa
**Posts:**9853**Joined:****Location:**Alpha Centauri

QuoteOriginally posted by: outrunNo, its not a square, if so,, then the solution would only be correct for a=1 Actually "a" stands for "Area", I forgot to mention that. It is definitely a square and a is its side, unless wileysw measured the radius in the units of area, which would be very wrong :-)a~

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