Bragging rites .... or being Mr Goofy!

Let me tell you something about myself without bragging.

Let me tell you something about myself without bragging. When I’m good in the smarts department I’m over the top, beyond the moon and across the universe but -- and here comes the hatchet -- when I goof I goof so seriously in such a major key that even Shakespeare winces and da Vinci shakes. So to cut the bs, this is to tell you that the English movies problem I posted a couple of weeks back had a wrong clue: namely, the eighth clue should have been “Turning blue (1995; 3)” and NOT “Turning blue (1990; 3)”  as was published. My bad.
This means all the huge handful of you who got only nine right (thanks to my gaffe you know who you are now) can have another go before we enshrine your moniker in letters of Lawrencium. Of course if you get the heading in the process too which was “Debut Eulogy (2017; 5)” and which no one even tried, there’ll be more brownie points.
 
THROUGHPUT
(The granddaddy of problems was: “If you take your mechanical watch to the mountains, will it run faster or more slowly than usual? Oh and if you don’t mind, why?”)
Time will pass quicker or rather the watch will run faster on top of a mountain due to gravitational time dilation. Time runs slower closer to massive objects. -- Dr Shyam L, orthoshyam@gmail.com
When a mechanical watch is taken to the mountains where the temperature is normally less than 5 degrees C, the metallic parts of the watch contract slightly because of which the watch tends to gain time. -- Narayana Murty Karri, k_n_murty@yahoo.com

In modern day mechanical watches, the balance wheel is made of Invar, an alloy with very low thermal expansion and the balance spring is made of Elinvar, an alloy without any change in elasticity over a wide range of temperature. Therefore, if you take a modern mechanical watch to the mountains, it will keep perfect time, unaffected by the change in temperature with altitude. -- Balagopalan Nair K, balagopalannair@gmail.com

Had it been a pendulum clock, the time period being inversely proportional to the sqrt of acceleration due to gravity would be more as ‘g’ decreases at high altitudes. Hence in the pendulum clock case the clock would be late. -- Nrusingha Behera, ncb123.age@gmail.com
A mechanical watch runs faster in the mountains because its balance wheel has less air to push around and, therefore, oscillates a bit faster. -- Dhruv Narayan, dhruv510@gmail.com
(The second problem, a reader submission about measuring four litres of milk, turned out to be way too easy-peasy with more than 75 right solutions. So we’ll just run the names of the first 10 correct ones this time. But hey Dr Ramakrishna Easwaran, drrke12@gmail.com, how about submitting some tougher puzzles next time?)

Abhishek Narayan, dudeabhi4u@gmail.com; Narayanan P S, narayananpsn@gmail.com; Ramesh Kumar, rameshkumarthayyil@gmail.com; Sambasivam S V, svssivam@yahoo.com; Shekar G P, shekargp@yahoo.com; Kshitish Krit Nanda, kritnanda@gmail.com; Murali S L, murali_sl@yahoo.co.in; Shashi Shekher Thakur, shashishekher@yahoo.com; J Vaseekhar Manuel, orcontactme@gmail.com; K K N Raj, kknraj2017@gmail.com.

(The third one was: “A skater skates a kilometre in three minutes with the wind, and returns in four minutes against it. What’s his speed for a kilometre if there’s no wind?”)
Secondary school algebraic problem. If the skater’s speed is assumed as ‘s’ and the wind speed as ‘w’, then s + w = 20 kmph (3 minutes per km) and s - w = 15 kmph (4 minutes per km). Adding both these equations, 2*s = 35 kmph which means s = 17.5 kmph. When 60 is divided by this, we get the answer as 3.4285 minutes. Hence if there is no wind, he can cover 1 km in 3 minutes 26 seconds approximately -- Sheikh Sintha Mathar, sheikhsm7@gmail.com
 
BUT GOOGLE THIS NOW
1. There are 100 marbles in a bag. They’re numbered 0 - 99. You keep drawing them out one at a time, noting its number and replacing it. On average, how many numbered 1 - 99 will you have to draw one or more times before getting to marble number 40?
2. Find a 10-digit number whose first digit is the number of 1s in the number, second digit the number of 2s in the number, etc. Answers can’t start with a zero.

Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)

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