A monk starts his journey from the base of the mountain early morning at 7 am and reaches the monastery at the top of the mountain at 7 pm. He followed the hilly route at a completely variable speed. He sometimes sat down to take rest too. He was fast at times and slow at other times. After giving the necessary message to the head monk, next day, fully rested, he started at 8 am to climb down. Once again, he walked at varying speed including taking rest at times. Since it was downhill though, he reached by 6pm. Can you prove that there was at least one clock time where on either day at the same clock time, he was at the same spot? [note that you do not need to find out when and where – that is indeterminate – just that there had to be a time when on either day at that time he was at the same spot]

There are 101 completely unbiased identical coins. You give your friend 50 and you take 51 of them. Both of you toss all the coins you have. What is the probability that you will land up with more heads than your friend?

You and your friend are sitting across a perfectly round table and have a bunch of identical quarters. You two will alternately place quarters flat on the table such that a quarter will not overhang the boundary of the table nor overlap on another quarter. Whoever runs out of space, loses. You go first. How will you ensure that you win?

You have a stone weighing 40 pounds. You have to break it up into 4 parts such that using those weights in a scale and pan balance you can weigh anything from 1 pound to 40 pounds (integers only) Example: if you broke them as 5,5, 7 and 23, you can get 2 by putting 7 on one side and 2 on another. What are those 4 weights?

How can you get 7 using only three 2s. You can use plus, minus, multiply, divide, square root, factorial, decimal point, log, “to the power of” and parentheses. As many times as you want. You can also put digits together to form … let’s say 22.

Using only two 4’s how would you get 64? You can use standard mathematical functions found on a calculator – plus, minus, multiply, divide, to the power, log, square root, factorial…. Cannot use trigonometry or any other digit.

You drive a car 30 mph on a 1 mile lap. How fast must you drive the 2nd lap to average 60 mph for both laps?