There’s this guy who’s a proud owner of a certain number of rabbits and also the proud father of three sons who for some reason are expert logicians.
So now all this guy needs is to believe he’s about to die so he can make a will to divide the rabbits among the sons, right? Right, except that he then also calls them together (the sons, not the rabbits) and tells them how many rabbits (not sons) he owns and adds that the eldest will inherit the most rabbits and the youngest the least with nobody having more than 10 rabbits, which as we all know is a crime.
Does he then whispers in each son’s ear how many rabbits he personally will inherit? Absolutely. After that he proceeds from the eldest to the youngest, asking each aloud if he can calculate how many rabbits each of his brothers will inherit and each replies, “No.”
He does it again and again each replies, “No.” But then the eldest son on being asked the question once more says, “Yes, each of the last two ‘noes’ (that’s the plural of ‘no’) gave me some information, and I now know (no plural of ‘knows’) how many rabbits each of us will inherit.” Aren’t you already wondering how may rabbits each son will get?
THROUGHPUT
(Here’s a cold turkey from a week old fridge that concerned matching two sets of 20 words each which you had to pair up with a dollop of streetsmart sussing.)
The only thing I could make out of TURKEY as a slang is a clueless person or a flop. This is sort of synonymous with BOMB. The other slang words of the same meaning I could match are: RAP - YAK (chatter); DAMAGE - TRASH (waste); RAW - GREEN (novice); JOINT - WEED (grass); DRAG - MAX (to the limit); CHILL - SQUAT (seat); HAIRY - CREEPY (unpleasant); PAIN - DRAG (burden); BOMB - TURKEY (Failure/Clueless); SQUARE - ZERO (stupid?). Could be OUT too (out of touch); CAN - JOHN (wc); KNOCK - SCRUB (cancel); BREAD - DOUGH (money); WASTE - SQUEEZE or TRASH (kill/destroy); THREADS - GEAR (clothing); PAD - DIGS (housing); RAG - SHEET (newspaper); RUG - MOP (hair); ZIP - SQUAT or ZERO? (nothing); COOLER - CLINK (prison). -- Saishankar Swaminathan, saishankar482@gmail.com
(The second problem was: “Consider the sum of the series: 1/2 + 1/3 + 1/4 + 1/5 + 1/6 + 1/7 + 1/8 . . . . After how many terms can we be certain that the sum exceeds 100?”)
The given series is a harmonic one without the first term, 1, and is divergent, meaning that it’s sum tends to infinity as the number of terms tends to infinity. The sum of the series for finite number of terms can be worked out by integration. In exponential form, this is n >= e^100 where e is the base of natural logarithm, called Euler’s number, whose value is 2.71828 (approximate).
This is a huge number, but finite and therefore, we can say that the sum of the series does exceed 100 for a finite, though very large, value of the number of terms. -- Balagopalan Nair K, balagopalannair@gmail.com
Since the series is divergent, albeit very slowly, one can, indeed, exceed any given number. -- Ajit Athle, ajitathle@gmail.com
(Incidentally here’s someone who also finally answered the pistol in space problem correctly, though conveniently omitted to tackle the second and more difficult part.)
. . . the reason I didn’t mail the answer sooner was NOT because it took time. It’s because (a) I live in a crap hole with no rich neighbour to steal WiFi from, and (b) I’m smack dab in the middle of my exams. My name is Rubin James, better known on the internet as Jimmy Evil, Lord of Supervillains. -- Rubcjazz, rubcjazz@gmail.com (What’s the matter Ruby on Rails, you scared of Kepler? Or should we wait till you flunk to get part II going?) (Continued in BGTN)
BUT GOOGLE THIS NOW
1. Meaning, what if that pistol was in orbit around Earth when it shot the bullet backwards at 10,000 kmph? This would put it in a higher orbit. Which means it would start slowing down to conserve angular momentum.
On the other hand the bullet would get into a lower orbit and thus increase its speed. Someone watching from Earth should then notice the bullet first catching up with the pistol and later overtaking it. Or what?
2. Divide the digits from 1 to 9 into three sets of any size. Must the product of the integers in one of the sets always exceed 71? If yes, how close to 71 can you get?.
Sharma is a scriptwriter
and former editor of Science Today magazine.(mukul.mindsport@gmail.com)