Forgot to post a puzzle on my flight back from DC.
Here is one I remember from my childhood days.
Think about a simple picture of a star with 5 corners (not 6). I have attached a picture. So, there are 10 points – 5 outside and 5 inside (I marked them 1 thru 10 in the picture). The goal of the puzzle is to check off as many of those points as you can. The process of how to check off is the following: You start from any unchecked point and then going in a straight line, skip the next point (checked or unchecked) and the next point you land on gets checked off. So, if you start from 8, you can skip 6 and check off 5 or skip 10 and check off 1. Then you start from another unchecked point and keep doing this. You always have to start from an unchecked point. Question is – what is the maximum number of points you can check off and how.
(as always, if you know or think have found the answer, send me a personal message)

Atypical week – returning home on Tuesday. Too tired to do the Thursday thinking… So, here is a simpler math puzzle. Using 8,8,3 and 3, can you get 24? You are allowed to use only plus, minus, multiply and divide. Strictly speaking, parentheses should be allowed too. But that is it. Private message me if you know/found the answer.

Familiar Thursday evening situation: On a flight returning home. Have not posted a puzzle in some time. So, here is one…
What is the next number in the following sequence?
4, 6, 12, 18, 30, 42, 60, 72, 102, …
(If you know the answer send me a personal message)
Disclaimer: I remember this puzzle vividly from my college days because after two days I simply gave up 🙁

The number 1210 is unique in the sense the first digit signifies how many 0s are there, the second digit signifies how many 1s are there, the third digit signifies how many 2s are there and so on… 21200 is another such number. Can you come up with a 10-digit number? (first digit shows how many 0s are there….. all the way to tenth digit shows how many 9s are there)

There is a 10 digited number. It has 2 each of the following digits – 0,1,2,3 and 4. Funnily enough, the two 4s are separated by 4 digits in between them; the two 3s are separated by 3 digits in between them, the two 2s are separated by 2 digits in between them… by now you have guessed the rest – the same thing for 1s and 0s. Can you find some of those numbers? (There are multiple answers)

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?