The October issue of the National Geographic magazine has a cover story on the next ‘Killer Flu.’ The story talks about a silent killer that is stalking birds and humans in southeast Asia. The ‘bird flu’ could be the next pandemic after the infamous Spanish Flu of 1918 that killed between 50 and 100 million worldwide. The mathematical twist to the flu tale is a prediction model that tells us what will happen if this virus, which causes bird flu in humans, goes out of hand and precipitates the next pandemic. The model paints a grim scenario: a rampaging bird flu pandemic could kill, in the worst case, up to 360 million people! The model is pretty robust, in mathematical sense, and the associated graphs of a rampaging pandemic show no signs of tapering off as it moves from one city to the other. The speed at which people move these days causes the infection to spread at a rate that is almost double of the flu pandemic in 1968. However, all is not lost in this war against flu, the health agencies worldwide are on alert and a vaccine is already on the shelf of chemists’ shops.
PUZZLE 1: I have five different sticks of different lengths, and I can use any three of them to form a triangle. I claim that none of these triangles will an acute-angled triangle. Am I right'
PUZZLE 2: Can the squares of a 1990x1990 chessboard be coloured black or white so that half the squares in each row and column are black, and cells symmetric with respect to the centre are of opposite colour'
PUZZLE 3: A group of children form two equal lines side-by-side. Each line contains an equal number of boys and girls. The number of mixed pairs (one boy in one line next to one girl in the other line) equals the number of unmixed pairs (two girls side-by-side or two boys side-by-side). Is the total number of children in the group divisible by 8'
Solutions on October 10
Soumava Chakraborty; Piyush Modi, Calcutta; Debasis Ganguly, Alumnus Software; Arun Kumar Sikder, Sibpur; Shivaprasad Bandyopdhyay, Purulia; Suvendu Bikash Bhattacharjee, Krishnagar; A.K. Saha, Jamshedpur
Sunita Sharma, Bokaro Steel City; P.K. Srivastava, Cal-91; Sunil Chatterjee, Andaman; Arun Kumar Chawla, Jharia; Anant Sinha, Cal-26; Promita Mullick, Noapara.
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Solution 1: 105 questions. Suppose he asks questions as usual, and then asks, “Did you lie to any of the last questions'” If the reply is a truthful no, then the answers were correct. If the reply is a lying no, then the answers were still correct. On the other hand, if the answer is yes, then the answers might or might not have been correct.
Solution 2: 23 stories. Let’s call stories with an odd number of pages odd stories and stories with an even number of pages even stories. There are 15 odd stories and 15 even stories. The odd stories change the parity of the starting page (in the sense that the following story starts on a page of opposite parity), whereas the even stories do not.
Solution 3: There are 210 pairs of towns. Each airline serves 10 pairs, so we need at least 21 airlines.