## Posts

### Fraction Brainteaser

Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions.  In total, Siddhant scores 25 out of 34.  Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34. Note that a) Vaibhav scores more than Siddhant b) Siddhant score better than Vaibhav in both individual topics -  5/6 > 20/25 and 20/28 > 6/9 How is it possible?

Source: Alok Goyal (Stellaris VP, Ex-Helion VC) puzzle blog Problem: A fast food restaurant sells dimsums in boxes of 7 and 3. What’s the greatest number of dimsums a person cannot buy. Generalize it for p and q where p and q are relatively prime. I loved the puzzle. Hope you enjoy it too.

### Law of Large Numbers Failed

Problem: There are two maternity hospitals in a town with 50 and 500 beds. Given full occupancy on a particular day, which of these hospitals is more likely to have equal no of boys and girls given probability of boys = probability of girls ? ‪ What would the answer intuitively be by #‎LawOfLargeNumbers‬? You would see #LawOfLargeNumbers does not seem to work here. How should the statement be positioned for #LawOfLargeNumbers to work?

Source: Alok Goyal (Stellaris VP) puzzle blog Problem: This is another famous puzzle in the Martin Gardner collection, and variations of this puzzle exist in different “sizes”. This particular one has been picked up from The Colossal Book of Short Puzzles and Problems, Puzzle 9.18. Replicating the puzzle as is. Lenox R. Lohr, president of the Museum of Science and Industry in Chicago, was kind enough to pass along the following deceptively simple version of a type of combinatorial problem that turns up in many fields of applied mathematics. A traveler finds himself in a strange town without funds; he expects a large check to arrive in a few weeks. His most valuable posession is a gold watch chain of 23 links. To pay for a room he arranges with a landlady to give her as collateral one link a day for 23 days. Naturally, the traveler wants to damage his watch chain as little as possible. Instead of giving the landlady a separate link each day he can give her one link the first day

### Soldiers in a Line

Source:  Alok Goyal's Puzzle Page Problem: In a line up of 10 soldiers, what is the least number of soldiers that can be picked in order of either ascending or descending heights? Assume that no two soldiers have the same height. Soldiers can be picked from anywhere in the line, but their order of standing cannot be changed.