Solution:

The best way to analyze the situation would be forcing a win for white when the black player plays anywhere but a corner square. Refer to the given figure for the current positions. Now, if black plays 7 to block the white player from having three in a row, white will move 5 to 6 and will win. But since you get to place only three markers, black can place the marker at 6 and white won't be able to add one more at 7 to win. And moving the 9 marker to 7 will take two steps.

But white can still get to square 7 before black is able to block him or form a three in a row. In this manner, no matter what black does, the white player can always win the game if he begins from the center square.

Solution:

You can easily understand what we did through the given figure. But if somehow, you are unable to understand, here is what we did. We just cut along the lines as shown. Remove the red parts from the square. Tilt it a bit and then place the cut portions as shown in the figure.

Solution:

There are sixty marks in the given figure, thus it is safe to assume that each mark represents a minute.

Now, the hour hand is on a mark when the minute hand is on [0, 12, 24, 36, 48]. When the minute hand is on a mark, the second hand is on noon. But the orange hand cannot be the second hand. (It would be onnoon and it would be eighteen minutes past/before a full hour.)

a) Purple is on 12. Green indicates twenty four minutes. orange indicates forty two [minutes] = 8 + 2/5 [hours] = 8:24
b) Purple is on 12. Green indicates thirty six minutes. orange indicates eighteen [minutes] = 3 + 3/5 [hours] = 3:36
c) Green is on 12 = 3:36
d) Green is on 12 = 8:24.

Please note that the watch could be rotated upside down as well.

Solution:

It is not as tough as it seems. The strategy is quite simple. You just have to pick up a card out of first three whenever you find a 9 or higher number.

Let us offer you a strong valid reason for the strategy. The probability that the four card kept below are below the number nine is 32*31*30*29 / 52*51*50*49 = 0.133
Thus in such case, you will lose $2 to $9 with equal probability = 0.133/8 = 0.0166

Let us now calculate the probability that one of the four cards is nine or even higher.
1 – 0.133 = 0.867
Now you will surely stop at the first sight of 9 or any value above 9 as per the strategy. Thus you have a chance of winning -1, 0, 1, 2, 3 with an equal probability = 0.867/5 = 0.173

In such case you stand a chance of winning overall amount of 0.14 every game you play.

Let us consider the other strategies. If you want to stop at the sight of 10 or above 10, the expected amount you will win per game will be 0.09 which is way below the present strategy. If you want to stop at above ten only, you will have an expected winning in negative.

Solution:

The person is leaving hospital after visiting his wife. His wife is on a life support system. The elevator has stopped due to the power cut. If there was an emergency backup generator functioning well, the elevator would have also be running. It stopped in between means that the life system support has stopped as well.

Solution:

Toy3 Toy6 | Toy1 Toy7 | Toy2 Toy5 Toy8 | Toy4