First a huge HUGE correction (like what was I thinking?). In the analogies problem given last week #(3) “Coffee : Chicory :: Leaf : ?” should read “Coffee : Chicory :: Seed : ?” Now for an announcement. Due to a huge build-up of solutions, this time’s Endgame will not feature any problem so that I can do some urgently needed housekeeping here. So let’s go.
THROUGHPUT
(The reader problem was: “At a party, we can hear our name being called out from a little distance, and sometimes we even know who’s calling. If the same ‘call’ is recorded on a smartphone and played on an amplifier can we also hear our name called?”)
The call would be difficult to hear, because our brain is able to perceive the difference between “useful” sound (like somebody calling us) and background noise. But electronic equipment cannot distinguish between noise and sound; both being just vibrations through a medium. -- Saifuddin S F Khomosi, Dubai
While recording and playing back, each time a sound loses a part of its main characteristics such as pitch and loudness. So we shall still be able to hear our name, though not as clearly as during the original call. -- Sheikh Sintha Mathar, sheikhsm7@gmail.com
(The second one was: “A stands 100 m south of B. B starts travelling towards the east at speed x, whereas A starts travelling at speed 2x in a direction always facing where B is at that moment. How much distance would B have travelled when he meets A?”)
In the general case where A travels at V m/s and B travels at u m/s as stated, the time taken by A to catch up with B = L*V/(V² - u²) where L is the initial separation. We’ve L = 100 m, V = 2x m/s and u = x m/s and thus T = 2*100*x/(4x² - x²) = 200/(3x) seconds. -- Ajit Athle, ajitathle@gmail.com
Let the time taken by B before he meets A be t minutes. Let the speeds of B and A be x and 2x meters/minute respectively. While B is travelling towards east, the path travelled by A would be in a north-east direction. Thus the paths travelled by B and A would form the sides of a right-angled triangle with hypotenuse being the path of travel of A, the path taken by B as one side and 100 meters as the second side of the triangle. Hence we get the relation
(2xt)^2 = (xt)^2 + (100)^2. Thus we have xt = 100/(square root of 3) = 57.733 meters. -- Narayana Murty Karri, k_n_murty@yahoo.co
(The gist of the third one was: How come water doesn’t fall out of a sponge?)
Water is held in the multiple cells because of surface tension of the water, which counters gravity. Squeezing breaks the surface tension. -- Dr Ramakrishna Easwaran, drrke12@gmail.com
A sponge is full of holes and can still hold water without draining off because of capillary effect. Just as water will move up a narrow tube. – Dr Shyam Lakshminarayanan, orthoshyam@gmail.com
The water goes in by capillary action. Then adhesion comes into the picture. Water molecules adhere to the sponge fibre on the surface of pores of the sponge. Simultaneously, surface tension also acts to hold the water molecules in the pores. The forces of adhesion and surface tension outmanoeuvre the gravitational force to retain the water. These forces get outmanoeuvred by higher external force of squeeze to force the water out to repeat the process. -- Abhay Prakash, abhayprakash@hotmail.com
(The fourth one is self explanatory.)
The two 13 letter words without using B, C, D, G, J, O, P, Q, R, S & U are the following: 1.
INATTENTIVELY; 2. INEXTENTIVELY. V V Murthy, varahamurthy1954@gmail.com (Sorry VVM but #2 is not a recognised word. – MS)
After some diligent Googling I could garner these three 13-letter words made up of letters that are devoid of any curves, all as straight as they come. (1) INATTENTIVELY; (2) INFINITIVALLY; (3) NEMATHELMINTH. Nemathelminth is any form of nematode worms that belong to the phylum nematoda. -- Balagopalan Nair K, balagopalannair@gmail.com
OH, AND INCIDENTALLY . . .
. . . don’t just give answers to the analogies problem; give reasons too. For example: Istanbul : Constantinople :: New Rome ::? The answer is “Byzantium” because that was the old name for New Rome just like Constantinople was the old name for Istanbul.
Sharma is a scriptwriter and former editor of Science Today magazine.
(mukul.mindsport@gmail.com)