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Extreme Tunnel Vision

E4
Let's say, at some time in the fictitious future, an enormous tunnel of 100 metres in diameter was dug through the Earth. A very large sphere of 80 metres in 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's 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?
 
DEAR MS
(Last 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?" - MS)
 
In-Hot-Water-Dept:
This is because of a chemical exothermic reaction that releases heat. Since the detergent is held in the palm, the palm feels hotter. It would also happen if the water were warmer.
- Nandu Trehan, nightnan69@gmail.com
 
As the detergent is mixed in water, an exothermic reaction takes place, releasing heat energy to the surroundings. This makes the hand feel hot. The warm water will raise the temperature bar further.
- Saifuddin S F Khomosi,
saif_sfk@hotmail.com
 
(The second was to find the next two numbers in the series 202, 122, 232, 425, 262, 728 - MS)
 
Number's-Up-Dept:
The next two numbers in the series are 292 and 1031. If we start at the first number 202 and see every alternate number (232, 262 and 292), the difference between two succeeding numbers is 30. So we have to add 30 to 262 to get 292. If we start with the second number and see every alternate number (122, 425, 728 and 1031), the difference between two succeeding numbers is 303. So then we have to add 303 to 728 and we get 1031.
- Niraj Nandish, nirajnandish
@icloud.com (Yes, but see a niftier
solution below - MS)
 
Look closely at the pattern of the digits of the given sequence (ignore the commas) and group them as two-digit numbers. You'll see 20 21 22 23 24 25 26 27 28 . . . Hence, the next two terms will be 293 and 031.
- Priyanka Awatramani,
priyankag1010@gmail.com
 
(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. However, 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?" - MS)
 
Who-Guards-The-Guard-Dept:
When the guard goes inside, start walking across. You will be halfway through when the guard comes out. Just before he comes out, turn around. Thus, the guard will send you 'back', while actually, he is sending you right where you want to go. Kind of ridiculous but it's the best I've got.
- Bawse Gautham,
gauthamgopinadh@gmail.com
 
I start from one end of the bridge and cover half the length in five minutes when the guard comes out. At that moment, I turn around and start walking towards the end from where I had started. The guard catches me and forces me to turn around and complete the remaining journey in the next five minutes.
- Ayan Joshi,
ayanjoshi@yahoo.com
 
ENDGAME(S)
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,
sheikhsm7@gmail.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 fills faster?

(Mukul can be reached at mukul.mindsport@gmail.com)