5 cars were travelling on a freeway. Each car stopped at exactly 2 red lights. Also each pair of cars stopped together at the same red light at some point. Show that at some instant at least 3 of the 5 cars stopped simultaneously at the same red light. via AMS math society puzzle corner
Monthly Archives for June, 2013
Amongst 524 nominees for the Nobel prize, the winners of the Nobel prize lived 1.4 years longer on an average. Why? (Hint: Correlation does not imply causation). - Via Tanya Khovanova's Math blog
There are N coins of which one is fake. The fake coin is either lighter or heavier than the rest. There are 2 balance scales that can be used in parallel. Each use of a balance will take 1 minute. Find the largest N and a strategy so that the fake coin can be determined in 5 minutes. via Tanya Khovanova's blog
There are 3 gold and 3 silver coins. These are distributed amongst A,B and C, 2 coins each. You are allowed to ask a single question to any one of the 3 people. The answers you may receive are "YES", "NO", "I DON'T KNOW". Using the answer, determine what coins person A has. via Tanya Khovanova's blog
You write 100 numbers in a row. Then you underline the following numbers: 1) The numbers that are positive. 2) Every number whose sum with the next number in the row is positive. 3) Every number whose sum with the next two numbers in the row is positive. Can the sum of all underlined numbers be zero? Can the sum be negative? A more general statement: n numbers are … Continue reading the story "Hundred numbers"
If x,y,z,w are four natural numbers such that xy=zw, can the sum x+y+z+w be prime? - via 60-odd YEARS of MOSCOW MATHEMATICAL OLYMPIADS
Can you represent 2013 as the sum of at least 2 positive integers so that the product of these positive integers is also 2013? via Manhattan Mathematics olympiad
Find 2 tetrahedrons ABCD and EFGH such that a) EFGH lies completely inside ABCD b) The sum of edge lengths of EFGH is strictly greater than the sum of edge lengths of ABCD. -- Via white board on packard floor 2.
Here is a variation of the poison wine puzzle: Suppose there are 1000 bottles of wine and one of them is poisoned. You have prisoners as test subjects. A prisoner will die within a maximum of 6 days after trying the wine. You want to find the poisoned wine in 6 days, while minimizing the expected number of prisoner deaths. Also, if the concentration of the … Continue reading the story "Poison wine variation"
Reposting a famous puzzle pointed out to me by prof. Thomas Cover. Suppose you are shown 2 envelopes and are told one envelope contains double the amount of money as the other. You are asked to choose one envelope at random and inspect it's contents. Then you are offered a choice: You either keep the money, or switch envelopes to get the money in the other … Continue reading the story "Two Envelopes"