The Boss is 90. On October 21, Martin Gardner celebrated his 90th birthday.

If you were wondering why a belated birthday notice is being posted, let me be honest and tell you that I was over-ambitious and trying to interview the guru of recreational mathematics. The interview did not happen, so I thought, ?Why let this occasion go by??

Let us raise our Klien bottles and M?bius strips to celebrate Gardner?s 90th and hope he scores a century. He has entertained us with recreational mathematics and made us think with his essays on science; it?s time we started something (please do not suggest a fan club) in his honour. I?m sure nothing would please Gardner more than if we did something for the population living in fear of the maths demon.

PUZZLE 1: Find the smallest positive integer such that when its last digit is moved to the start of the number (for instance, 1234 becomes 4123) the resulting number is larger than, and an integral multiple of, the original number. Numbers are written in standard decimal notation, with no leading zeroes.

PUZZLE 2: An urn contains a number of coloured balls, with equal numbers of each colour. Adding 20 balls of a new colour to the urn would not change the probability of drawing (without replacement) two balls of the same colour. How many balls are there in the urn? (Before the extra balls are added.)

A boy has four red marbles and eight blue marbles. He arranges his 12 marbles randomly, in a ring. What is the probability that no two red marbles are adjacent?

Solutions on December 13

CORRECT ENTRIES

November 15

Animesh Majumder, Cal-97; S.K. Choudhary, Durgapur; Dhrubajyoti Daityari, Santoshpur; Dhruba Roy, Cal-94; Subrato Ranjan, Bhubaneswar; Sunil S. Shah, Cal-20; Sohamjit Das, FAPS; Radha Mohan Kejriwal, Raniganj; Binita Devi, Dibrugarh; Shrenik Rungta, Julien Day School; Bankim Chandra and Sumanta Tosh, Serampore; Devi Chand Khemka, Siliguri; Pratik Agarwal, IEM-Salt Lake; Swarnabha Mukherjee, Cal-91; Soumyajit Pati, Purulia; Ma-hul Bhattacharya, Ranchi; Dipanjan Saha, Cal-75; Malay Mandal, IIT-Kgp; Shyamala Ramakrishnan, Cal-45; Tripurjoy Ghosh, Cal-1; Sugata Lahiri, Guwahati; Olivia Banerjee (email).

CORRECT ENTRIES

November 8

Devasis Hazari, Bilaspur; S.P.S. Jain, New Delhi; S.K. Choudhary, Durgapur; Shardha Singh Deo, Purulia; Dhrubajyoti Daityari, Santoshpur; Sourabh Gupta, Chandigarh; Bijan Kanti Ghosh, BEC-Sibpore; Debasish Roy, Barrackpore; S.Krishnaiyer, Cal-8; Pratik Agarwal, IEM-Salt Lake; Suhail Ghosh, Santoshpur.

PUZZLE CRACKED

Solution 1: First, the man takes the goat across, leaving the wolf with the cabbage. Then he goes back. Next, he takes the wolf across. Then the man goes back, taking the goat with him. After this, he takes the cabbage across. Then he goes back again, leaving the wolf with the cabbage. Finally, he takes the goat across.

Solution 2: To find the correct switch (1, 2, or 3), turn switch 1 to ?on? and leave it like that for a few minutes. After that you turn switch 1 back to ?off?, and turn switch 2 to ?on?. Now enter the room. If the light bulb is lit, then you know that switch 2 is connected to it. If the bulb is not lit, then it has to be switch 1 or 3. Now touching the light bulb will give you the answer: if the bulb is still hot, then switch 1 was the correct one; if the bulb is cold, then it has to be switch 3.