經典拆地雷遊戲

數字表示比鄰八格的地雷總數。問地雷在哪裡？

Interesting Result from Equation Solving

Consider

x - 1 = 0

The only root of the above equation is 1.

However, when we take
x = 1
and take square of both sides, then

x² = 1
x² - 1 = 0
(x - 1)(x + 1) = 0

Consequently, x = 1 or -1

TWO roots are found, but actually one of them SHOULD BE REJECTED.

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Don't Be Afraid

More than One root found. Don't Be Afraid.

Not all the roots are real. Don't Be Afraid.

Among the real roots, some should be rejected.

Just do it.


More than One girl friend got. Don't Be Afraid.

Not all the girl friends are real. Don't Be Afraid.

Among the real friends, some should be rejected.

Just say it.


More challenging problems ahead. Don't Be Afraid.

Not all of them are real challenges. Don't Be Afraid.

Most of them will be eventually solved.

So just believe it.

We just Don't Need To Be Afraid.

Events which are "Equally Likely to Happen"

Determine which of the following is true:

1. Mr. Chiu plays chess with Fat Chuen. He will either win, lose, or get a draw. As a result the probability that Mr. Chiu win is 1/3.

2. Mr. Chiu plays the famous lottery style game "Mark Six". He selects 6 numbers out of a possible 49 and it costs him $5. He will either win or lose. The probability of getting a prize is 1/2.

3. There are 2 red and 3 white balls in a bag. One ball is drawn out randomly. The probability of getting a red ball is 1/2.

4. A coin is tossed 2 times. Denote a head by H and a tail by T. There are 3 possible outcomes: 2H, 1H and 1T, 2T. Consequently the chance of getting 2 heads is 1/3.

5. 2 dice are thrown. The sum of the 2 numbers faced up is lying between 2 and 12. The probability of getting a 'double six' is hence 1/11.