Solution
No, the law would not work.
In obedience to the laws of chance, the first children born to all the women would tend to divide evenly between boys and girls. The mothers of the boys would have no more children. The mothers of the girls would then have their second round of children, and again half would be boys and half girls. Once more the mothers of the boys would drop out, leaving the other mothers to have a third round of children. In each round, the number of girls would tend to equal the number of boys, so the ratio of the boys to girls would never change.
Solution
The only way that the first player can be sure of winning is by taking three pennies from the bottom row on his first move.
Any play that leaves one of the following patterns is sure to win:
One coin in each of three rows.
Two coins in each of two rows
Three coins in each of two rows
One coin in one row, two in another, three in a third
If you keep these four winning patterns in mind, you should be able to defeat an inexperienced player every time that you have the first move, as well as every time that he goes first and fails to make the correct opening move.
This game can be played with any number of counters in any number of rows. The game has been completely analyzed by using the binary system of arithmetic.
Solution
The joker in Nikhil's numbers is that his time categories overlap so that the same periods of time are counted more than once. To give one example, during his vacation period of 60 days he both ate and slept. This eating and sleeping time is counted in vacation period and also counted separately in his eating and sleeping times for the entire year.
This fallacy of overlapping categories is a very common one in statistics, especially medical statistics. You may read that in a certain community, 30% of the people have vitamin A deficiency, 30$ have vitamin B deficiency, and 30% have vitamin C deficiency. If you conclude from this that only 10% of the people have no deficiency of these 3 vitamins, then you are making same kind of faulty reasoning that Nikhil is giving to Professor Sony Thomas.
Solution
Turn the page upside down, and circle three 6's and three 1's.