Ever since I mentioned that some people were complaining their emails Ids were being reverse phished after being published here, some of you have been requesting that those Ids be withheld. No problems there but at least let us know where you’re from (like city, town, village, planet, etc) so others don’t think you’re a completely Willy Wonka.
A number of birds, either black or white, are on a wire with at least one bird of each colour. We also know that whenever two birds are separated by four or seven other birds, these two birds are the same colour. (1) What is the maximum number of birds on the wire, and how are they aligned? (2) What difference would it make if we changed the 4 to a 5? (Continued in BGTN #2)
THROUGHPUT
(The Old Man River was: “A bag contains either a black or white counter. A white counter is now put in, the bag shaken, and one counter taken out. This is white. What is the probability of the next counter coming out of the bag also being white?”)
After drawing the white counter, the probability of the remaining counter being white is 2/3. Because, the white counter that was drawn is either (a) the counter that was originally in the bag; in that case the remaining counter is white, probability 100% or (b) the white counter added to the counter in the bag; in that case the probability of the remaining counter being white is 50%. Thus, the probability of the counter, that comes out next, being white is 2/3. -- Balagopalan Nair K, balagopalannair@gmail.com
Magnify the problem 100 times. Now, in the first draw, we will have 75 whites and 25 blacks. Ignore the 25 blacks, as they do not qualify for the second draw. In the second draw, we have 50 whites and 25 blacks left. Ergo, white has a 66.6 percent chance. QED. -- Dhruv Narayan, dhruv510@gmail.com
(The second problem was: “Why not attach a suction pump to a pot and suck out the air above the water level, and the water would come to a boil faster – thereby saving energy. How come this technology has not been pursued instead?”)
To maintain lower pressure suction has to be continuous to take away steam. Then temperature will not increase but it is the higher temperature which is required for cooking not the boiling of water. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com
The reverse of the Papin’s Digester is useful if the purpose is to only boil the water. But to cook food we need to raise the temperature. So it is not useful. In fact, mountaineers face this problem as the water tends to boil away before the food is cooked.-- Dr Shyam L, orthoshyam@gmail.com (Yes, Mallesh K S, ksmallesh@gmail.com, you aced it too.)
(The third one was: “There are 5 full bottles of water, 5 half-full and 5 empty. How do you divide both the water and number of bottles equally between three people?”)
Supposing that one full bottle of water contains one unit, there will be a total of 7.50 units in five full bottles and five half. With five empty bottles, total number of bottles is 15. This is to be divided equally among three people which means that each person should get 2.5 units in five bottles. Now, half a unit of water each in five bottles will be 2.5 units. Give away the five half bottles to person #1. Pour half a unit each from the five full bottles to the five empty ones. Give one set of five to person #2 and the other to person #3. -- Sanath Kumar T S, sanathkumarts1958@gmail.com (Yes Lipika Muthu, geelip@ymail.com of grade 8, you also tried.)
(Among the first five who also got it right are: Dr. P Gnanaseharan, gnanam.chithrabanu@gmail.com; Sriram Venkatachalam, sriramvenkatachalam@protonmail.com; J Vaseekhar Manuel,
orcontactme@gmail.com; Abhay Prakash, abhayprakash@hotmail.com; S V S Sivam, svssivam@yahoo.com)
BUT GOOGLE THIS NOW
1. From the surface of Earth if you throw a small ball straight up, does it take longer to go up or come down? (You know how gravity’s such a “drag” etc.)
2. (Continued from top) (3) If we replace the 4 and 7 by arbitrary numbers A and B, under what condition can the number of birds be infinite? (4) If the number of birds is not infinite, what is the maximum number of birds on the wire for a given A and B?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)