In school I remember, during one of those unimaginably boring algebra classes, my friend who sat next to me -- Sanjeeve or Dilip or something his name was -- would from time to time alleviate the tedium by asking me if I could draw a six pointed star without lifting my pencil from the page or going over one line twice. I never could but since I never had any closure either let’s have a relook at it now.
A typical five-pointed star is drawn in continuously connected but not repeated line segments such as AC, CE, EB, BD, DA and these segments have to alternate a constant number of points (skipping one point in this case). Given that there is only one way to draw a five-pointed star, and no way to draw a six-pointed (in continuous lines, that is) and two ways to draw a seven-pointed one, how many different ways are there to draw a 1,000-pointed star?
THROUGHPUT
(For oldtimers unlike some of us who are new in this, the problem was: “Let’s say it takes 10 seconds on average to type each number (spelt correctly in English). How long before you hit a C?”)
The first time C will appear when the numbers 1, 2, 3, ... are typed out in words is in OCTILLION. Depending on whether you are in the US or elsewhere, OCTILLION is 1 followed by 27 zeros. Accordingly, it will take you roughly 3.17*10^19 years in the US (or 3.17 x 10^40 years elsewhere). -- Rajagopalan K T, ktremail@gmail.com
When you type the numbers ONE, TWO, THREE and so on, the first time you use the letter C is when you reach ONE CRORE. So you have to type one crore numbers. And this takes ten crore seconds (10,00,00,000 seconds). This works out to be 3 years, 2 months, 17 days, 9 hours, 46 minutes and 40 seconds. After this period you are free, -- Dr P Gnanaseharan, gnanam.chithrabanu@mail.com
(The second one was: “The pronunciation of “polish” is different when the first letter is capitalised as in “Polish”. How about at least four or more words like that?”)
Most of them seem to involve proper nouns. August/august, Rainier (mountain name)/rainier, Tangier (in Morocco)/tangier (taste), Reading (city in UK), Nice (city in France), Natal (region in South Africa), etc. -- Saishankar Swaminathan, saishankar482@gmail.com
These words are heteronyms, a sub-category of homographs. The spelling of these words is the same, but they are pronounced differently and have different meanings. Common words in this category are: WIND, LEAD, LIVE, MINUTE and AUGUST. -- Saifuddin S F Khomosi, Dubai
The four words NATAL, NICE, READING and JOB are pronounced differently when capitalized and used as proper nouns. It is not enough that the words are capitalized; it is essential that the words have to be used as proper nouns. -- Rajagopalan K T, ktremail@gmail.com
(The third one was: “What’s the next number in the series: 0, 0, 9, 1, 0, 55, 0, _? Incidentally -- this sequence is developed from the first seven even numbers.”)
For the next in number series, the clues are to look for Roman numerals in the English words of the even numbers. -- Ravichan Ramadurai, raviramad@gmail.comWrite down the even numbers in plain English starting from 2. We have TWO, FOUR, SIX etc. Remove all alphabets other than C, D, I, L, M, V & X (letters that figure in Roman numerals). Now try interpreting the left over alphabets and write the number they represent in decimal system. Assign a zero if there are no letters left. TWO doesn’t have any Roman numeral letters. A SIX, after removing other letters, becomes IX, i.e: 9. Without the clue, it would have been so difficult! -- Saishankar Swaminathan, saishankar482@gmail.com
BUT GOOGLE THIS NOW
1. Some words contain smaller versions of themselves. For instance INDOLENT contains the letters I-D-L-E, in order. What are the hidden synonyms in the following? ABIDE, ALLOCATE, ASSEVERATE, ASTOUND, CALUMNIES, CATACOMB, DEPOSITORY, DESTRUCTION, ENCOURAGE, HONORABLE, ILLUMINATED, INEFFECTIVE, REVOLUTION, SCOUNDREL, TRANSGRESSION, UMPTEENTH, UNSIGHTLY.
2. I put two sealed envelopes on a table. One contains twice as much money as the other. You pick an envelope and open it. You are then given the opportunity to trade envelopes. Should you?