A popular magazine recently featured what our celebrities have been reading in the year that’s going to end soon. Going through the reading list of the President of India, the Prime Minister, noted writers, chess world champion, political bigwigs, and other famous Indians I found only three titles on science. Of them, one bordered on mathematics. Many of those covered in the article often lament on the state of science education in the country, but when it comes to reading habits, popular science or mathematics do not figure in their scheme of things. So don’t go by what they say. Please try yourself to find out the most interesting titles on math that has been published recently, and take a dip into a sea of pleasure.

PUZZLE 1: On Numberland each of the natives is one of two types: Truth-Tellers who always tell the truth, or Liars who never tell the truth. Numberland is governed by a Council of Elders who will only answer questions that have numerical answers. In fact, the only answers they give are whole numbers, either zero or positive. They will never give an answer greater than the current number of council members. This number can vary daily, but is never less than 4 or more than 40. Also, the council will only answer questions whose correct answers are independent of who is asked (for example, no questions such as “How old are you?”). One day three native students, Ann, Bob and Cal, were given an assignment by their teacher to question the council. They each asked a question, which was answered by every council member. Afterward they reported to their teacher and made the following statements:

(1) Ann: I asked the council how many of them were Truth-Tellers. (2) Bob: I asked the council how many of them were Liars. (3) Cal: Those statements are not both true. (4) Ann: All of the answers I received were different (no two equal to each other). (5) Bob: All of the answers I received were different (no two equal to each other). (6) Cal: At least two of my answers were different (not equal to each other). (7) Ann: The sum of my answers is a palindrome. (8) Bob: The sum of my answers is a palindrome. (9) Cal: The square root of the sum of my answers is not less than the number of council members.

What was the number of council members on that day?

Solutions on January 9

CORRECT ENTRIES

December 12

Swarnabha Mukherjee,Cal-91; Zia-ul-Hoque, ISI-Baranagore; Henna Sethi, St. Xavier's- Cal; Manish Bakshi, Cal-28; R.K. Nandi, Durgapur-4; Madhab Dutta, Purulia; Vipul Vaid; Navnit Kumar, NIT-Jalandar; A. K. Majumdar, Cal- 106; Sreechandra Banerjee, Cal-19; Chanchal Kumar Roychowdhury, Chandannagore; Arnab Kr Sadhukahn, CMCC-JU; Sidharth Udani, Cal-25; Samik Ghosh, Cal-12; Ravi Raja, Cal -20; Arundhati Dasgupta, Barrackpore; Rajesh Das, Cal-57; Subhash Chaklader,

PUZZLE CRACKED

Solution 1: You divide $113 (in whole $ increments) into seven bags as follows: 1, 2, 4, 8, 16, 32 and 50. Clue to the solution: If we want to divide any amount into the minimum number of bags, the distribution should follow a series ina geometric progression, with the first term of the GP being 1 and the common ratio 2. That is, the first bag should contain Re 1, the second Rs 2, the third Rs 4, the fourth Rs 8, the fifth Rs 16, the sixth Rs 32, the seventh Rs 64 and so on. Of course, there can be many such solutions. In our example, in which we had $113 to divide into seven bags, the last one should contain $50.

Solution 2: Basil, who came in seventh, lost the game he played against Waldo who came in third.

The puzzles appeared on December 12