Vanishing point camaraderie between old foes!

Want to find out the height of a molecule in a few minutes? Get a large, rectangular pan, a piece of straight stiff wire and a drop of oil. Fill the pan with water to the brim till it almost overflows. Then take the wire and lay it across the breadth of the pan close and parallel to one edge so that it portions off a smaller rectangular area. In this region gently place the drop of oil. It will immediately spread across the water’s surface till it occupies the whole of the smaller rectangle.

Now start sliding the wire towards the other edge carefully so that the oil film occupies a progressively greater area. A time will come when there just won’t be sufficient oil left to cover the water and gaps will start appearing. Stop at once. At this point the depth of oil is exactly one molecule thick. Measure the length and breadth of this region. Since the volume of oil can easily be figured out and the length and breadth are known, it’s a matter of school math to work out the height. So can it be done?
Not interested? Right, let’s try something boring instead. A fair die bearing the numbers 1, 2, 3, 4, 5, 6 is repeatedly thrown until the running total first exceeds 12. What’s the most likely total that will be obtained?
 
THROUGHPUT
(The Old Wives’ problem was: “A solar system has three planets revolving around the central sun. To begin with, all four are in a straight line. Etc, etc, etc. What is the least number of weeks which must elapse before they are in a straight line again?”)
After 6.75 weeks, the innermost planet will be at 270 degrees from its starting position. Middle planet will also be at 270 degrees from starting position. Outermost planet will be at 90 degrees from starting position. Thus all four will be in a straight line at this time. Two of the planets will be on one side of sun and the third planet on the opposite side. Ravi Nidugondi, ravi.nidugondi@gmail.com
There are two different answers for two different logics. (1) 6.75 weeks if we don’t bother about opposite halves; (2) 13.5 weeks for the same half. -- Ganesh Ram Palanisamy, 1969ganram@gmail.com

(The second one was: “What three digits are represented by X, Y, and Z in this addition problem? XZY + XYZ = YZX?”)
X is 4, Y is 9 and Z is 5. The giveaway is in the middle column. If Z + Y were to be Z, then Y must be either 0 or 9. If it were to be 9, there must have been a carry of 1 when adding the last column. Since the solution has Y in the hundreds place, it cannot be zero. So Y = 9. Since Y is 9, there must be a 1 carried from the middle column. Therefore in the first column X + X + 1 = 9. This gives the value of X as 4. Now in last column 9 + Z = 4, must be actually 9 + Z = 14. This gives Z = 5. Finally we have 495 + 459 = 954.

Dr Ramakrishna Easwaran, drrke12@gmail.com

Given the condition, XZY + XYZ = YZX, we can say 100X + 10Z + Y + 100X + 10Y + Z = 100Y + 10Z + X = 0 (or 199X = 89Y - Z). Substituting values for X = 1 up to 9, it becomes clear that X = 4, Y = 9 and Z = 5. -- Saifuddin S F Khomosi, Dubai.
(Among the first five who also got it correct are: K Sathyadev, sathya2008k@gmail.com; Pratyusha Ramesh, pratyusharamesh@gmail.com; Ramakrishna Bhogadi, rambhogadi@gmail.com; Raghunath K, rakhunath.k@gmail.com; Dhruv Narayan, dhruv510@gmail.com.)
(The third problem was: “What is the only temperature that is a prime in both Celsius and Fahrenheit?”)
The only temperature that is prime in both Celsius and Fahrenheit is 5 deg C which is equivalent to 41 deg F. If negative is also considered -5 deg C is equivalent to 23 deg F which is also a prime. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com

BUT GOOGLE THIS NOW
 1. In a certain country it’s legal for second cousins to marry. So can third cousins, fourth, fifth and higher cousins. Anita and Bob are third cousins but cannot marry. Why? (Incidentally, If they were not related, they would be perfectly eligible.)
 2. How many pairs of prime numbers are there whose sum is 999?

Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)