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"19. Find a truly end of the sentence: If your reflection looks on me then A) you look on mine reflection B) my reflection looks on you C) you look on me D) I look on your reflection" "25. A house has 10 rooms. Ten boys stay in different rooms and count the number of doors in them. After...

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why lol?

p is a prime number. Proof that \sum\limits_{i = 1}^{p - 1} {cos\left( {\frac{{2\pi i}}{p}} \right)} = - 1.

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The answer is D. But why?

Give three positive numbers a, b, c such that a+b+c=3. Find maximum value of following expression \frac{a}{a+\sqrt{3a+bc}}+\frac{b}{b+\sqrt{3b+ca}}+\frac{c}{c+\sqrt{3c+ab}}.

I can understand. Thank you so much! I colour as following

Can you explain more clearly? Thanks a lot.

A Kangaroo has a large collection of small cubes 1 \times 1 \times 1. Each cube is a single colour. Kangaroo want to use 27 small cubes to make a cube 3 \times 3 \times 3 so that any two cubes with at least one common vertex are of different colours. At least how many colours have to be used?

Thanks to your clue, I have another solution: \triangle ABD \backsim \triangle ACB \Rightarrow \frac{AB}{AC}=\frac{AD}{AB} \Rightarrow AD=\frac{AB^2}{AC}=\frac{60^2}{80}=45 \\ \Rightarrow DC=35 \Rightarrow BD = 35.

I think you mean TriABD ||| TriACB. I have just known how to use LaTex in this forum. Thank you very much!

Let ABC be a triangle having \angle{B} = 2 \angle{C}, AB = 60 cm and AC = 80 cm. BD bisects \angle{B}, D \in AC. Find the length of the internal angle bisector BD.

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Please help me to solve Q20 in AMC 2012 Junior!