It’s called the Mpemba Effect because of Tanzanian student Erasto Mpemba. In 1963 he was in secondary school when he got up to ask a visiting professor of physics: “If you take two similar containers with equal volumes of water, one at 35 °C and the other at 100 °C and put them into a freezer, the one that started at 100 °C freezes first. Why?” Predictably, the whole class sneered in ridicule but the one person who didn’t was the visiting professor who later actually experimented on the issue back at his workplace and confirmed Mpemba’s finding. They published the results together in 1969 while Mpemba was studying in college. The story provides a dramatic parable cautioning scientists and teachers against dismissing the observations of non-scientists and against making quick judgements about what is impossible and what isn’t.
However, here’s the thing; in the 45 years since the Effect’s publication scientists are still not in complete agreement why the phenomenon takes place and at least six different theories -- ranging from evaporation, convection and frost to supercooling, thermal conductivity and dissolved gases -- have been proposed. Yet still no consensus. Do you have any thoughts on why such a counterintuitive thing should happen? Write in.
If not, try this: ABCD is a rectangular sheet of paper (A at top left, rest clockwise). EF and GH are lines perpendicular to AB such that AE = EG = (AB)/4. AX is an arbitrary line through A meeting BC at X. The paper is folded such that point G falls on AX and corner A falls on line EF at point Q. What is the ratio of the angles XAD and QAD?
(The problem was: “A travels at the rate of x kilometres an hour, while B travels at the rate of x minutes a kilometre. Obviously, if x is 30, then A is much faster; while if x is 3, then B is much faster. What must be the value of x for A and B to be travelling at the same speed?”)
A is travelling at 60/x mint/km according to the problem, so this equals the speed of B which is x mint/km if they have to go with equal speed which gives us the solution, that is “square root of 60” and it is 7.74596669241 mint/km for B and 7.74596669241 km/ hr for A. -- Mahaveer Chowdary, email@example.com
Others who also got it right early are: Narayana Murty Karri, firstname.lastname@example.org; Murali S L, email@example.com; Ramakrishna Bhogadi, firstname.lastname@example.org; R Viswanathan, email@example.com; Ramesh, firstname.lastname@example.org; yaramala kotireddy, email@example.com; Arpan, firstname.lastname@example.org.
(The other problem concerned four people playing a bridge like game and you had to determine which suit was the high one after being given some conditions.)
The card game problem. W X Y and Z have cards C H D, C S S, C H H and S D D respectively. If the tricks have to satisfy the conditions mentioned C (clubs) has to b the high suit. Assuming that W leads, because W is mentioned first, whether he leads H or D the three tricks will be the same. W takes a trick with S H S C, X takes a trick with H C H D and Y takes a trick with D S C D. Details of how the cards fall avoided for brevity but, briefly, if W leads H, X takes the first trick by trumping and plays S which W trumps and plays D which Y trumps. If W leads D, Y takes the first trick by trumping and plays H which X trumps and plays S which W trumps. -- Balagopalan Nair K, email@example.com
(And finally the problem about paddling upstream with your trusty guide keeping time and a logbook . . .)
The answer to the boat and paddling puzzle is as follows. 10:25 -- We are again abreast of the blue jetty; 11:55 -- Once again abreast of blue jetty; 12:45 -- We reach the camp; 13:30 -- The shirt reaches the camp. -- Dr P Gnanaseharan, firstname.lastname@example.org (Yes Subin, email@example.com, you got it right too. -- MS)
BUT GOOGLE THIS NOW
1. Look carefully at a wall clock’s hour and minute hands. Now ask yourself -- how many times in a 24 hour period do the two overlap?
2. In the film Gandhi, the Mahatma seeing a poor ill-clad woman sitting downriver from him, takes off his chaadar, crumples it and throws it into the water. As it floats towards her the chaadar stretches out on the water. What makes it open out in such a manner?
Sharma is a scriptwriter and former editor of Science Today magazine.(firstname.lastname@example.org)