A lot of people have written in saying what I actually had was something called herpes zoster. I know that, but chicken pox makes it sound so much sillier and laughable whereas herpes zoster sound like I’m looking down the business end of a lingering and hateful terminal malady that’s going to take the stuffing out of life and shove it down death’s throat. Even shingles is funner.
So let’s listen to the met department instead: “Today’s weather is different from yesterday’s. If the weather is the same tomorrow as it was yesterday, the day after tomorrow will have the same weather as the day before yesterday. But if the weather is the same tomorrow as it is today, the day after tomorrow will have the same weather as yesterday.”It is raining today, and it rained on the day before yesterday. What was the weather like yesterday? (Note: The prediction was correct!)
THROUGHPUT
(The first problem of this year was: “Set a circle rolling around the interior of a circle of twice its diameter and follow a point on the former circle. An English inventor exploited this principle to produce an engine in which a steam piston drives a wheel? Who?”)
Matthew Murray (1765 - 1826) was a British designer and inventor who came upon the hypocycloidal concept. He used a smaller gear wheel of half the diameter of the outer ring. This wheel would roll inside the bigger ring. As the piston rod, attached to the smaller wheel, moved forward and backward, the linear motion would be converted to circular motion. A working version (still works!), made by 1805, is available in Thinktank, Birmingham Science Museum. -- Saishankar Swaminathan, aishankar482@gmail.com
(The second one was: “You run on a level road for some distance, then run to the top of a hill and return home by the same route. You run 8 mph on level ground, 6 mph uphill, and 12 mph downhill. If your total trip took two hours, how far did you run?”)
Distance uphill = 6*t1; Distance downhill = 12*t2. But both the distances are the same, so 6*t1 = 12*t2 or t1 = 2*t2. Now, average speed (uphill and downhill) = (6*t1 + 12*t2)/(t1 + t2) = (6*2*t2 + 12*t2)/(2*t2 + t2) = (24*t2)/(3*t2) =8 mph. The speed on level road is also 8 mph. So the total average speed of the whole journey is 8 mph. If it takes 2 hours to complete the trip, then the total distance I ran is 16 miles. -- Saifuddin S F Khomosi, Dubai.
One can complete 16 miles within 2 hours. The average speed of 6 mph and 12 mph for same distance is 8 mph. So the aggregate average is 8 mph. -- Purushothaman Chandrathil, purushothamanchandrathil1969@gmail.com
(Among the first five who also got it right are: Gnanaseharan Ponnaiah, gnanam.chithrabanu@gmail.com; Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com; Balagopalan Nair, balagopalannair@gmail.com; Nrusingha Behera, ncb123.age@gmail.com; Gopunatarajan Natarajan, natarajangopunatarajan3@gmail.com.)
(The third problem was: “Each point on a straight line is either red or blue. Is it possible to show that it’s always possible to find three points of the same colour in which one is the midpoint of the other two?”)
Choose two points of the same colour, say blue. Call these A and B, and let C be their midpoint. If C is blue then we’re done. If C is red then mark points D and E as shown such that AD = AB = BE. Now if D or E is blue then we’re done, because these produce the blue triples DAB and ABE. And if D and E are both red then we have DCE, a red triple. So there’s no way to assign colours to these five points without producing some monochromatic triple. -- Dhruv Narayan, dhruv510@gmail.com
Pick two points (A and B) of the same colour (say red). Consider the point C such that B is the midpoint of AC. Then D such that A is the midpoint of BD. Then E such that E is the midpoint of AB. If at least one of C, D or E is red, then three equally spaced red points have been found. If C, D and E are blue, then they are three equally spaced blue points. Hence possible. -- Abhay Prakash, abhayprakash@hotmail.com
BUT GOOGLE THIS NOW
1. If you cut a rubber band to make one long strip and pull it from both ends in opposite directions will there always be a point on the strip that doesn’t move?
2. The digits 123456789 can be arranged to form 362,880 distinct 9-digit numbers. How many of these are prime?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)