Here’s a fun thing. 111,111,111 × 111,111,111 = 12,345,678,987,654, 321. Look at it carefully and wonder in shock and awe before figuring it out with an instant Aha! solution. However, the next one’s going to require a little more of a (M)aha! working out solution.
Two numbers -- not necessarily different -- are chosen from the range of positive integers greater than 1 and not greater than 20. Only the sum of the two numbers is given to person A and only the product to person B. Here’s their subsequent cell phone conversation: A: “I see no way you can determine my sum”. B: (one hour later) “I know your sum”. A: (some time later) “Now I know your product”. What are the two numbers?
THROUGHPUT
(The problem concerned an 80m dia sphere dropped down a 100m dia tunnel through the Earth with a smaller stone simultaneously dropped down a smaller tunnel through the sphere. What would be the joint configuration when they reached the end?)
The sphere and the stone would execute simple harmonic motion about the centre of the Earth with a time period of 84.5 minutes, reaching a maximum speed of about 7.9 km/s at the centre, at which point although there is no force acting, they will move towards the other side due to inertia and will eventually come to rest (briefly) at the other open end of the tunnel; After which both will fall back in again and continue the process ad infinitum. If the air friction is assumed, then it will slowly reduce the velocity of travel and finally they will come to rest at the centre of the Earth. – P S Guruchandran, psguru@bheltry.co.in
When sphere reaches the other end, the COG of the stone will be at the surface of the Earth at the other end. -- Ravi Nidugondi, ravi.nidugondi@gmail.com
(Regarding the analogies problem 47 people replied -- with only three (yes, just three) getting all 12 correct. Sixteen got only one or two wrong but the heaviest hassle happened with #11 with almost everybody thinking the answer was Maurice Ravel. Alas!)
The answers are: (1) Strip is to Mobius as Bottle is to KLEIN; (2) Thought is to Action as Obsessive is to COMPULSION; (3) Mice is to Men as Cabbage is to KING; (4) Sword is to Damocles as Bed is to PROCRUSTES (a toughie); (5) Jekyll is to Hyde as Eloi is to MORLOCKS (my eight-year-old daughter knew that); (6) 4 is to Hand as 9 is to SPAN (measuring unit in inches); (7) Hollow Victory is to Pyrrhic as Hollow Village is to POTEMKIN (another toughie); (8) Easy Job is to Sinecure as Guiding Light is to CYNOSURE; (9) Leg is to Ambulate as Arm is to BRACHIATE; (10) Astronomy and Physics is to Astrophysics as History and Statistics is to CLIOMETRICS); (11) Language Games is to Ludwig as Piano Concerto for the Left Hand is to PAUL (Wittgenstein brothers; Paul lost his right arm in WW-I); (12) Set of Sets Not Member of Themselves is to Russell as Darkness of the Night Sky in an Infinite Universe is to OLBERS. -- Charanjit Singh Pardesi, cspardesi@gmail.com (Along with Balagopalan Nair K, balagopalannair@gmail.com and Shashi Shekher Thakur, shashishekher@yahoo.com.)
(The third problem was: “If a year consists of 365 days then how many times does the Earth rotate during this year? The answer is 366. But the question is why?”)
The time taken for the Earth to rotate 360 degrees is 23 hours 56 mins and 4 secs. So in a day there is a difference of 3 minutes and 56 seconds. In a year the difference is 23.92 ours accounting for an extra rotation. -- Saishankar Swaminathan, saishankar482@gmail.com
We know that in a year the Earth takes 365.2422 solar days to revolve around the sun. Astronomers use a sidereal time-scale based on Earth’s rate of rotation measured relative to the fixed stars rather than the Sun. One rotation takes a mean sidereal day which is 23 hours 56 minutes 4.0916 seconds or 23.9344699 hours or 0.99726958 mean solar day. So, the number of rotations in a year = 365.2422/0.99726958 = 366. -- Abhay Prakash,
abhayprakash@hotmail.com
BUT GOOGLE THIS NOW
1. To get a peeled hard-boiled egg into a bottle just drop a burning taper in and the vacuum created by the loss of oxygen sucks the egg in. But the O2 loss is compensated by the production of CO2 and water vapour. So what sucks the egg in?
2. What colour is hidden in the following sentence: “One dancer I see is out of step.”
— Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)