We’ve just been discussing our health,” says A, “and found that between us we share the same five complaints, and the same prescribed tablets for them. Each of us has two complaints, but no two have both the same, and no more than two of us take each sort of tablets. For instance two take red tablets, two blue, and so on. I don’t have green ones. I take one lot the same as E, but they are not yellow, and I do not take kidney tablets.”
B says, “I don’t have green tablets. One heart patient also has tablets for sleeplessness.” C says “I don’t have kidney tablets. I take one lot the same as E which are not for the heart. I don’t take blue ones.” D says, “I don’t have heart trouble. My tablets are not yellow. Those who take green tablets do not also take blue ones.” E says, “I take white tablets which are not for the heart. The ones with nerves do not have indigestion, and nerve tablets are not yellow.” So what colour are the heart tablets? Who takes them for nerves?
Throughput
(The solution to the superannuated stumper which had not been forthcoming finally came. In case your mind no longer serves you right it concerned a pistol travelling at 10,000 kmph and vaguely doing all kinds of things with a bullet fired back at you.)
How the pistol and the bullet fired from it appear to an observer depends on the observer’s frame of reference. If he is in one that moves at the same speed as the pistol, the pistol appears static and the bullet as moving with the muzzle velocity. Whereas, if the observer . . . (okay we get it -- MS). As to the question of you being right behind the pistol and pulling the trigger, you may do it if you have a death wish.
Because when it is fired, you happen to be in the same frame of reference with the pistol, and so the bullet will hit you at 10,000 kmph. -- Balagopalan Nair K, balagopalannair@gmail.com
(The second one was: “Without Pythagoras what’s the area of a square whose diagonal is 5?”)
Draw the other diagonal; both the diagonals bisect each other. Now you have got four right angled triangles whose adjacent sides are 2.5 units each. The area of one triangle is 2.5*2.5*0.5 square units. This multiplied by 4 will give the total area of.12.5 square units. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com
The diagonals of a square bisect each other at 90 degrees, dividing the square into four equal right-angle isosceles triangles. Each of the equal sides is half the diagonal. Area of each triangle becomes (1/2)(5/2)(5/2) = 25/8. Area of the square becomes 4*25/8 = 12.5. It can also be found out by trigonometry. Each side is 5 sin45 or 5 cos45 that is 5/sq root(2). Area becomes 25/2 = 12.5. Mr. Pythagoras not required here. -- Abhay Prakash, abhayprakash@hotmail.com
(Among the first of zillions who also nailed it are: Nrusingha Behera, ncb123.age@gmail.com; Parameshwaran Iyer, drvnp78@gmail.com; Shyam Lakshminarayanan, orthoshyam@gmail.com; Prof S Manikutty, manikuti@iima.ac.in; Shubhashish Mohanta, shubhashishmohanta@rediffmail.com)
(The tertiary trauma was about dates as they are written in India and the US and what percentage of them in a year are ambiguous because of this confusion?)
The ambiguous dates are 1 to 12 but we have to exclude the date corresponding to the number of the month as for example 3rd March is written the same way in both systems. So in all 12 months there are only 11 ambiguous dates. That gives 132 out of 365 days. This much I can figure out with my God given computer but the percentage is something I cannot say without a calculator that computes it to 36.16%. Or does that devious streak in MS require us to calculate the percentage in a leap year (36.06%)? -- Dr Ramakrishna Easwaran, drrke12@gmail.com (Yes Binata Mohanta, binatamohanta@rediffmail.com, and A V R Rao, raoavr@gmail.com, you got it right too.)
But Google This Now
1. If in rectangle ABCD there is a point E (not coincident with any of the vertices) such that AE, BE, CE and DE are all distinct integer lengths, what is the minimum value of AE + BE + CE + DE? – (Submitted by Ajit Athle, ajitathle@gmail.com)
2. A and B have two identical drinks consisting of 30 ml whisky, 60 ml water and one ice cube each. One of the drinks is lethally poisoned. A gulps it down and B lingers over it for half an hour. None of them dies. Whose drink was poisoned?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)