Chalk It Up Again ...jog your memory!

Sheikh Sintha Mathar at sheikhsm7@gmail.com emails to ask if I’m so forgetful that one of the problems (“What is the next number in the series: 1, 1  1, 2  1, 1  2  1  1, 1  1  1  2  2  1, ?”)          which appeared in March 2015 in these hallowed halls of higher academe had also dittoed itself in October 2014 and laments the repetition has happened in less than six months. So what can I say except take me out to the Court of Lost Appeals and sue me for a million bucks in bitcoins or, pending that, goosestep me to some forgotten backyard lot and 9mm me between the eyes.

 But just for that though, I’ve also decided to deliberately rerun yet another problem which most of you had conveniently blindsided your eyes to less than that same half a year earlier. Here it is: “A perfect sphere made entirely of chalk, rolls on a uniform flat surface at a constant speed. The chalk is transferred from the sphere to the surface at a uniform rate. If the sphere rolls in a straight line until there is nothing left of it to roll, approximately what shape will be seen on the flat surface?” (Please note that those who had not solved it in the last six months will be taken to the same court of appeals or goosestepped to a similar lot. However if you still can’t solve it, I’ll still understand.)

THROUGHPUT

 (The leftover problem was: “If an army column 40 kilometres long advances 40 kilometres while a dispatch rider gallops from the rear to the front, delivers a dispatch to the commanding officer, and returns to the rear, how far has he to travel?”)

 The dispatch rider has to travel a distance of square root of (2 x (40)^2) + 40 km = square  root of (3200) + 40 = 56.5685 + 40 = 96.5685  km. -- Dr  K Narayana Murty, k_n_murty@yahoo.com (Wing Commander Raju Srinivasan, rajusrinivasan@gmail.com, also nailed it and added: “I enjoyed this workout, though my wife cursed me -- and you -- for spoiling her Sunday!)

 (Regarding the time travel and time machine problem which is too long to repeat here, a lot of people thought the number 5 was the same upside-down and that led to their utterly rapid demise. However others correctly realised that only 0, 1, 6, 8 and 9 can be stood on their heads without a yoga instructor in charge. Examples follow.)

 Well the dude is 65 now. Three years later he’ll be 68. He then gets into the machine and comes out as 89. He waits for two more years when he becomes 91. Enters the machine again, and BAM! He’s turned into a 16-year-old. This reasoning does sound ridiculous, but it was just off the top of my head. Will email a better one if I think of it. (Don’t bother, it works fine as it is -- MS) -- Abhi Vakyl, vakyl.abhi@gmail.com

 Blah, blah, blah . . . Then in another 12 years he can again become 16. He waits for 3 years and at 19 he enters the machine and comes out as 61. Then he waits for 7 years and at 68 he enters the machine and comes out as 89. Then he waits for 2 years and at 91 he enters the machine and comes out as 16. Thus he can keep becoming 16 in every cycle of 12 years. -- Abhay Prakash, abhayprakash@hotmail.com

 (The third problem ran something like this: “If a donut – okay, okay dough-nut as some have Britishly pointed out -- shaped piece of metal is heated, does the hole in the middle expand, contract or stay the same?”)

 The hole in the middle will expand. This principle is used by horse-cart drivers. They make a metal rim of slightly smaller inner diameter (than the wooden cart wheel), then they heat the rim. The rim expands and is then put around the wooden wheel to make it durable. -- Athira Anand, athiraanand1@gmail.com

 When a glass jar’s screw-top metal lid is stuck, we turn the jar over and dip it in hot water so the lid can expand relative to the glass and it becomes easier to unscrew. What we are really doing is expanding the hole of the lid. Similarly, when you heat up a doughnut-shaped metal, the hole in the middle expands. -- Ramesh S Mahalingam, ramesh@idealmc.com

BUT GOOGLE THIS NOW

 1. A bowler takes three wickets in three different overs but it’s still a hat trick -- how? Though it sounds like a puzzle, it’s actually happened in test cricket! – Submitted by A V Ramana Rao, raoavr@gmail.com

 2. If you rapidly unroll Sellotape in a dark room, you can see a brief glow along the line where the tape is being spun from the roll. Why?

Sharma is a scriptwriter and former editor of Science Today magazine.

(mukul.mindsport@gmail.com)