Let’s say at some time in the fictitious future an enormous tunnel of 100 metres diameter was dug through the Earth. A very large sphere of 80 metres diameter was then constructed and a tunnel dug through it from one side to another along the diameter. The large sphere was then brought near the opening of the Earth tunnel and held such that its opening and the Earth tunnel opening were in a straight line. A very small stone was dropped into the sphere tunnel at the same instant that the sphere was dropped into the Earth tunnel. What would be the position of the stone in the sphere tunnel when the sphere reached the other end of the Earth tunnel?
(The last but not least week’s problem was: “Take some detergent powder in your palm and place it inside a bucket of cool water. As the powder rises up, the hand feels hot. Does it make any difference if it’s done in warm water?”)
When water is added to detergent powder, an exothermic reaction takes and the detergent forms micelles in water releasing thermal energy and hence the hand kept in the bucket of cool water feels hot. When detergent is used in warm water, the hand kept in the bucket feels hotter than when it is kept in a bucket of cool water. -- Narayana Murty Karri, email@example.com
Some substances release heat when dissolved in water and some lower the temperature, such as ammonium chloride. This is known as heat of solution and could be positive or negative. In this case, detergents are exothermic when dissolved in water and the temperature of water would rise from whatever it was, whether cold or warm. -- Gadepalli Subrahmanyam, firstname.lastname@example.org
(The second was to find the next two numbers in the series 202, 122, 232, 425, 262, 728, ?, ?”)
This looks too easy, maybe because I am looking at it wrongly. However, I am sticking my neck out and giving the solution I have arrived at. The series apparently is made up of two series: 202, 232, 262 with 292 as the next term and 122, 425, 728 with 1031 as the next term. Hence, the next two numbers in the series are 292 and 1031. -- Balagopalan Nair, email@example.com
(At least 50 people got the same answer in the same convoluted way. Among them the first five are: Shubhashish Mohanta, firstname.lastname@example.org; Jagan Nathan, email@example.com;
RVVS Murty Racherla, firstname.lastname@example.org; R.K Bhagat, email@example.com; Sanath Kumar T S, firstname.lastname@example.org. However, gaze now upon a more elegant solution.)
Fantastic one. When I removed the comma and started slicing the digits 1, 2 at a time, the solution stared at me. The sequence starts from 20 and goes on to 21, 22 . . . written three at a time. The next two numbers are 293 and 031. -- Saishankar Swaminathan, email@example.com (Yes Guruchandran P S, firstname.lastname@example.org you got it right too. -- MS)
(The third problem was: “You can walk across a bridge in 10 minutes. But a guard in a room at one end won’t let you cross. But, he stays inside for five minutes and then comes out to inspect for five minutes. If he catches you, he forces you to go back. So how do you go across?”)
Assume you are at the near end and want to go across. As the guard goes into the room, start walking. At the end of five minutes, make an about turn and start walking towards the near end. The guard, on seeing you will catch you and force you to go back to the far end. A nice puzzle! -- Dr P Gnanaseharan, email@example.com
My wife had a different take on this. “Why walk? Just run across in five minutes!” -- Dr A K Bhat, firstname.lastname@example.org
BUT GOOGLE THIS NOW
1. In a 24-hour digital clock with hh:mm format displaying time from 00:00 till 23:59, how many times in a day will the display be exactly the same as its mirror image? (Note: 10:01 will not be the same in the mirror image, due to the space between 0 and 1. It will look like 10:0 1). Also, what if it is a 12-hour clock? (Submitted by Sheikh Sintha Mathar, email@example.com)
2. There are two water tanks of equal capacity with same sized outlets for water connected to two taps. One tank is just above a bucket and the other is 10 metres above another bucket. Both taps are opened at the same time. Which bucket will fill faster?
Sharma is a scriptwriter and former editor of Science Today magazine