The good news is you don’t really have to be a Magnus Carlsen with 2800 plus Elo points to ponder the vagaries of the following chess problem although knowing how to play chess at a moderate kitchenette level helps. The bad news is if you’ve never heard of Edward de Bono you might be in trouble. So here goes.The rules of chess are changed as follows. White and Black alternately make two legal moves starting with White. Assume Black has a winning strategy which White knows about. Can we say that even if White does not win he or she can always guarantee a draw?
THROUGHPUT
(Looks like the hare-brained scheme with rabbits up for grabs from many moons back also had a lateral solution or two besides some other heroic efforts on the side.)
The owner of rabbits whispered in the ears of his sons that the eldest would get half of the total number of rabbits, the second 1/3rd and the youngest 1/9th. When he asked each son aloud whether they could calculate how many each would get, they could not answer because they were getting fractions when 17 is divided by either 2, 3 or 9. When both the second and the youngest son again did not know, the eldest got an idea. He brought one additional rabbit making a total of 18. Then he took 9 rabbits, gave 6 rabbits to his younger brother and 2 rabbits to his youngest brother and returned the extra rabbit. -- K Narayana Murty, k_n_murty@yahoo.com
(The other problem was: “A man can walk up a moving ‘up’ escalator in 30 seconds. He can walk down the same moving ‘up’ escalator in 90 seconds. His walking pace is always the same. (a) How long would it take for him to climb up the escalator if it is stationary? (b) How long would it take for him to go up the moving escalator if he stood still?”)
By simple relations, we get, d/a + b equals 30 and d/a - b equals 90 hence d/30 shall be equal to a + b equals thrice a - b. Hence on solving we get a equals 2b where a is man’s speed. Hence on substitution, we get d/a as 45 seconds, when escalator is stationary and d/b equals 90 seconds when man is stationary. -- Bitu Nayak, 2998b2nayak2998@gmail.com
If the speed of man is m mt/sec and the speed of escalator is e mt/sec, simple substitution would indicate that the man is walking at twice the speed of escalator. So: (a) equals 45 seconds; (b) equals 90 seconds. -- A V Ramana Rao, raoavr@gmail.com
(Among the first five to also get it correct are: Ramakrishna Easwaran, drrke12@gmail.com; K Sathyadev, sathya2008k@gmail.com; Shashidhara Sultanipur, shashidharasnpwd@gmail.com; K Balaji, mayavarathan29@rediffmail.com; S V S Sivam, svssivam@yahoo.com)
(The third problem was about a tied up balloon partially filled with sand and water. The question was why it could not be squeezed past a certain point no matter the force.)
At first the mixture takes up the vacant space still there in the balloon. Once this is filled, most of the pressure is taken up by the sand and hence the balloon does not have much stress coming on it. (Unlike if it is filled with water, when the water readily transmits the pressure on to the balloon.) -- Prof S Manikutty, manikuti@iima.ac.in
The situation is exactly like what one experiences at a beach. Compacted sand under the feet suddenly seems to “melt” when it comes in contact with water. When you press on the sand + water filled balloon the pressure in the water rises and it makes the sand sort of a gel inside the water. When water escapes from between the sand particles, the particles get compacted and there is increase in frictional forces which leads to that gritty, solid feel. The harder you squeeze the firmer it will seem. -- Dhruv Narayan, dhruv510@gmail.com
BUT GOOGLE THIS NOW
1. Can anyone devise a general procedure so that ‘n’ persons can cut a cake into ‘n’ portions in such a way that everyone is satisfied he or she has at least 1/n of the cake – preferably leaving no excess bits?
2. A is standing 100 metres south of B. Now B starts travelling due east at speed x, whereas A starts travelling at speed 2x in a direction that always faces where B is at that moment. How much distance would B have travelled when he meets A?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)