Now that the World Cup has softly and silently vanished and you know the winner because you’re reading this one week later, I still don’t know the same -- not because I was not welded to the flatscreen but because I’m writing this one day earlier. Yet just to get even, the answer to the following soccer problem is unknown to you but known to me. So bite dust!
Each of four football teams M, A, T and H played every other team once. Though each team had one win, one loss and one tie, none of the matches had the same final score. M, A, T and H scored 4, 2, 3 and 2 goals and allowed 2, 2, 4 and 3 goals respectively. Determine the results of all the matches.
(This is regarding the mildewed problem of syncing light and sound in film theatres since light travels so much faster to reach audiences.)
Back in the olden days, the Greeks made seats out of limestone, which reflects high frequency sounds extremely well. But my simple answer would be to place speakers in every corner and have soundproof walls so that it does not vibrate too many times. Limestone saved too! -- Lipika Muthu, firstname.lastname@example.org
This problem is even more pronounced (ha, ha!) in a drive-in theatre where the screen is even farther than a regular theatre and is addressed (ha, ha again!) by providing individual speakers to each car. -- Kishore Rao, email@example.com
I guess my father and the rest of his age watching Scarlett O’Hara in the 1940s on the silver screens were so bewitched by her that they cared two hoots about lip-sync (same applies to the ladies watching Clark Gable). Theoretically, recording at a fractionally higher speed and playing it at a trifle slower speed would solve the problem. At an entirely different level, the human brain processes auditory information faster than visual and so the auditory stimulus arriving 0.14 seconds later is processed at the same time as the visual image that came in earlier. -- Ramakrishna Easwaran, firstname.lastname@example.org
(The second one was: “Below are 13 five-lettered nouns, each of which has had two of its letters removed. In total there are 26 letters from A to Z. The remaining letters in each word are in the correct order. They are: clh, dir, ine, eba, ual, toe, yat, coh, rea, okr, aor, ree, sam”)
Very interesting. Here they are: CLOTH (OT), DIARY (AY), INDEX (DX), ZEBRA (ZR), QUAIL (QI),
STOVE (SV), YACHT (CH), COUGH (UG), FREAK (FK), JOKER (JE), MANOR (MN), REBEL (BL) and SWAMP (WP). -- Saishankar Swaminathan, email@example.com
Answers to the second question are CLASH, DAIRY, SWINE, ZEBRA, USUAL, STOLE, YACHT, COACH, TREAD, JOKER, ACTOR, RESET, and STEAM. -- Rekha G, firstname.lastname@example.org
(Among the first five others who also got it right are: Varaha Murthy, email@example.com; Shashi Shekher Thakur, firstname.lastname@example.org; Hema Parthasarathy, email@example.com; Sudha Narayan, Sunayana19@gmail.com; Saifuddin S f Khomosi, Dubai)
(The third problem: “One of five friends takes 1/N of the pizza. Then one of the five ate a slice which was 1/19th of the whole. What were the sizes of the slices of the rest of them?”)
The shares are 1/2; 1/3; 1/9 and 1/342, obtained by Fibonacci’s greedy algorithm for transforming rational numbers into Egyptian fractions. After 1/19 is taken away, 18/19 is left. Next integer in 19/18 is 2. So, start with 1/2. Now, 18/19 - ½ = 17/38. Next integer in 38/17 is 3. So, we take 1/3. Now, 17/38 - 1/3 = 13/114. Next integer in 114/13 is 9. So, take 1/9. Now, 13/114 - 1/9 = 1/342. Here we go. 1/19 + ½ + 1/3 + 1/9 + 1/342 = entire pizza. Odd habit indeed! -- Abhay Prakash, firstname.lastname@example.org
There is no unique solution. The sum of four slices must be 18/19 of the whole. Therefore denominator of each of the fractions must be a multiple of 19, two possible solutions are 1/76, 1/171, 1/228, 1/342 and 1/380, 1/665, 1/1330, 1/522. -- V K Bargah, email@example.com
BUT GOOGLE THIS NOW
There are a few 9-letter words in English that still remain a valid word even when each of their letters is successively removed. Got one? Or two? Good. Now what’s a similar 10-letter word?
Sharma is a scriptwriter and former editor of Science Today magazine.(firstname.lastname@example.org)