Professional thievery....... and eternal love for the Bard!

The A-One of all bards (good one, no?) may not have liked the following puzzle but at least he would have been grateful that even those who claim to grace our halls of higher academe can still be croo

The A-One of all bards (good one, no?) may not have liked the following puzzle but at least he would have been grateful that even those who claim to grace our halls of higher academe can still be crooks. With that behind us, let’s move forward.

Six professors had been to the library on the day that a rare book by Shakespeare was stolen. Each had entered once, stayed for some time and then left. If two were in the library at the same time, then at least one of them saw the other. Police questioned the professors and gathered the following testimony: Ashok said that he saw Bhaskar and Elsie in the library; Bhaskar said that he saw Ashok and Kumar; Annie claimed to have seen Devan and Kumar; Devan said that he saw Ashok and Kumar; Elsie testified to seeing Bhaskar and Annie; Kumar said he saw Annie and Elsie. One of the professors lied!! Who? There is a mathematical solution but I am searching for some alternates. (Submitted by Dr Vijayakumar Ambat, vambat@gmail.com)

THROUGHPUT
(The fresh start to the older year was: “You get to toss a coin until it lands tails. The number of lashes you get equals the number of coins you end up tossing. How many lashes do you think you can actually expect to get?”)

The probability of the first toss of a fair coin resulting in a head = (1/2). The probability of the second toss resulting in a tails = (1/2). Since these two are independent events, the required probability for one head followed by one tails in two tosses of the coin = (1/2)(1/2) = 1/4. Thus one can expect a tails in the fourth toss of the coin after three tosses. Therefore one can actually expect to get four lashes for three heads followed by a tails. -- Narayana Murty Karri, k_n_murty@yahoo.com

(The second problem was: “At 12 noon everyday a ship leaves port A and sails to port B across a vast ocean. Simultaneously another ship leaves port B and sails to port A. The ocean crossings take seven days and seven nights in either direction. How many ships will a ship leaving port A today pass at sea by the time it arrives in port B?”)

The solution to the shipping problem is 13. There may be 15 points, including the starting and ending, as it requires to meet ship from the other direction. But at starting and departing ports it does not cross the other. Because the starting and departing time will be the same. -- Purushothaman Chandrathil, purushothamanchandrathil1969@gmail.com

On its way from A to B, the ship will cross 13 ships coming from the other end, B. It will also possibly sight two more ships, though cannot be said to cross it: one, the ship from B that is just docking in when our ship leaves A; and the second that is just leaving B when it arrives at B. -- Bala Narayanaswamy, mail2nary@gmail.com

(The third one was: “I drove this car 20,000 miles and used five tires equally in accumulating the mileage. How many miles’ wear did each tire sustain?
After 4000 miles stepney is put in tyre 1 and tyre1 taken out. After 8000 miles tyre 1 is put in tyre 2 place and tyre 2 taken out. After 12000 miles tyre 2 is put in place of tyre 3 and after 16000 miles tyre 3 is put in place of tyre 4. At the end of 20000 miles all four tyres would have run 16000 miles. In simple terms we can calculate by taking four tyres at any time for 20000 miles which gives 80000 tyre-miles. Divide this by 5 tyres share we get 16000 each. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com

20000 miles translate to 80000 tyre-miles. With five tyres equally used, this works out to 16000 miles per tyre. -- Saishankar Swaminathan, saishankar482@gmail.com
At any point of time, we use only four out of five tires, which is 80%. So 80% of 20000 miles is 16000 miles. Tire or Tyre? -- Ganesh Ram Palanisamy, 1969ganram@gmail.com

BUT GOOGLE THIS NOW
1. You get out of your house, run on a level road for some distance, then run to the top of a hill and return home by the same route. You run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. If your total trip took two hours, how far did you run?
2. Each point on a straight line is either red or blue. Is it possible to show that it’s always possible to find three points of the same colour in which one is the midpoint of the other two?

Mukul Sharma

Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)

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