CORRECT ENTRIES CORRECT ENTRIES PUZZLE CRACKED
- Published 23.10.06
Lakshminarayanan Mahadevan, who finds joy in “discovering the sublime in the mundane,” has been awarded the George Ledlie Prize by the President and Fellows of Harvard College. “As an applied mathematician who breaks down the typical disciplinary boundaries in both his research and teaching, Maha personifies the nature of the renaissance scholar,” said Venkatesh Narayanamurti, dean of Engineering and Applied Sciences. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, has wide-ranging interests that centre around the applications of mechanics and mathematics to materials response, biology and geology; he places particular emphasis on phenomena visible to the naked eye and closely tied to experiments or experience. Mahadevan created a media stir in January 2005 when he and his colleagues solved the riddle of how the Venus flytrap snaps up its prey: The plant uses stored elastic energy to operate its curved leaves.
PUZZLE 1: On a remote island all of the natives belong to one of two tribes: the Brights, who are so brilliant at numerical calculations that they always get the correct answer, and the Braves, who bravely rush in to do calculations beyond their ability and never get the right answer. (The Braves are not entirely stupid: they can do simple counting and comparing of numbers, but they always get arithmetic calculations wrong.) Both Brights and Braves pride themselves on their complete honesty. They always tell the truth, or (in the case of Braves) at least what they believe to be the truth; they never purposely tell a lie (unlike the folks on some of those other islands).
One day a group of natives was playing a game of Numberskulls. There were 5 players and a moderator. The moderator, who was a Bright, painted a 3-digit number on each of the players’ foreheads, so that each could see all numbers but their own. All 5 of the numbers were different. The moderator would ask them questions in turn about the numbers they could see, and from the answers they would try to deduce what number was on their own forehead. The first to do so was the winner. What follows is a record of the game, with questions omitted and players designated by letters.
Solutions on November 6
K Sengupta, Cal- 19; Ranjan Nandi, Durgapur; Pankaj Bucha, Cal- 17; Samagata Bandhopdhyay, Cal-101; Sidharth Udani; Amartya Chakraborti; Calcutta-700031; Ravi Raja, Cal- 20; Anil Gupta, Salkia
K Sengupta, Cal- 19; Dipak Singh, JIS, Kalyani; Kumardip Sen; Subrata Kumar Chatterjee, Cal- 94; Aniket Basu Roy; Somesh Chaturvedi; Deepak Kumar, Howrah; Sailesh Jha, Shyambazar; Anup Bandhopadhyay, Behala
The response this week (October 9) was great. Brainstormer K. Sengupta was methodical in his approach. The solution is given below.
Solution: The unique highest possible score is 7, and it can only be obtained by answering the last question wrong!
Hint: Let us consider Q2 which can have only two correct answers, A or D. If it’s A then it forces the following answers Q: 1 2 3 4 5 6 7 8 A: C A C D D D and now none of the four answers for Q3 will be consistent with the others! If the answer for Q2 is D then Q: 1 2 3 4 5 6 7 8 A: D C D. This leaves us with B as the only choice for Q1, Q: 1 2 3 4 5 6 7 8 A: B D B C A D But this cannot give a score of 8 since the answer for Q6 is wrong! Thus a score of 8 is not possible. Follow the same method for each clue logically and you will get the answer.