Before we go on to the problem we are about to go on to, allow me to teach you a little about the refined art and science of cheating which I leaned a long time ago in school and college in order to fudge through my exams and collect more degrees than a thermometer. The problem in question is actually accessible on the internet (like what isn’t?) but through sincere hard work and honest perspiration I’ve modified it so much that even my sainted dead aunt wouldn’t be able to locate it anymore. However, if you still can then kudos to you because then, like Aishwarya Rai or Julia Roberts, you’re just worth it!
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?
THROUGHPUT
(The dementia case problem was about nine workers who want to discover their average salary. But no one wants to disclose how much he or she gets. So what to do?)
All you need to do is write a random number on a paper and give it to the second worker. The second worker adds his real salary to this number and hands over the total amount to the third worker. Workers three to nine continue the same way (adding their real salaries to the running total). When the ninth worker is finished, he passes over the total to you. You cleverly subtract the random number you entered at the start and add your real salary; and then divide the grand total by 9. -- Saifuddin S F Khomosi, Dubai
This solution is not quite optimal because the workers can still make some inferences about their co-workers’ maximum salaries. For example, if I give worker #2 the number 701,229, he knows that my salary cannot be higher than that. It can be improved by allowing the random number to be negative -- in that case no inferences are possible, and the math still works. (MS).
(The second one was: “Challenge a friend or foe to put the digits 1-9 in order so that the first two digits formed a number that was a multiple of 2, the first three digits were a multiple of 3, and so on.”)
The answer is 381654729. If number is “abcdefghi”, start with 5 which has to be in 5th place e for the number to be divided by 5. d has to be even and abcd divided by 5 should give reminder of 1 or 2. Hence d is either 2 or 6. Now looking at other places where even number digits are required h has to be also 2 or 6 to be divisible by 8 and preceding number being odd. b and f have to be the left out even numbers 4 or 8. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com
An interesting aside: The number 987654321, the number we get by arranging the digits in decreasing order, satisfies the conditions for all places except for the seventh. -- Balagopalan Nair K, balagopalannair@gmail.com
(Among the first five who also got it right are: Purushothaman Chandrathil, purushothamanchandrathil1969@gmail.com; Aruna Menon, mansuk78@gmail.com; Abhay Prakash, abhayprakash@hotmail.com; Narayana Murty Karri, k_n_murty@yahoo.com; Seshagiri Row Karry, srkarry@yahoo.com.)
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The third problem was: “Find the next term in the series that completes the set: 15, 91, 82, 46, 61, 84, 59, 78, ?)
This was meant to be tricky and it was. Looking at the numbers, the first thing that dawned on me was not to try any numerical formulae! But that left me nowhere. I thought of ages of PMs, Presidents, popular rhymes, country codes, etc. Finally the periodic table did the trick. The series consists of atomic numbers of all elements whose symbol start with P in ascending order (P, Pa, Pb, Pd, Pm, Po, Pr, Pt). The next in line is 94 representing Plutonium (Pu). -- Saishankar Swaminathan, saishankar482@gmail.com
BUT GOOGLE THIS NOW
1. I drove this car 20,000 miles and used five tires equally in accumulating the mileage. How many miles’ wear did each tire sustain?
2. How many people must be in a room in order for the probability to be greaterthan 1/2 that at least two of them have the same birthday? (Meaning the same day of the year although the year may differ.)
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)