Don’t ask me how they do it but in this fictional country boys and girls are born in strictly equal proportions. The King however, favours girls and wants to increase their number. So he issues an edict saying that any woman bearing a son would in future be banned from having any further children. His logic is that some families would therefore consist of multiple daughters but only one son. So far so good.Several years go by and soon the King has begun to tear his white balding hair out in black transplanted chunks because his census takers report back to him that the weird fictional country he thinks he rules in reality still contains an equal number of boys and girls. So where did his Majesty’s methodologically faultless logic sputter and die an unmourned death?
THROUGHPUT
(The Mother of all Hubbards puzzle was: “If you’re driving and notice that there’s a car in front of you with licence plates that read IXMNIZ. Can you guess the person’s occupation?” And one more about permutations of licence plates.)IXMNIZ sounds like “I examine eyes” and hence the person driving the vehicle ahead is either an OPTICIAN, an OPTOMETRIST or an OPHTHALMOLOGIST. -- Ajit Athle, ajitathle@gmail.com
The registration will look as follows: (One letter unique for the year): (3 digits): (3 letters). Total combinations possible in a year is: (10*10*10)*(26*26*26) = 1000*17576 = 17576000. For each three-letter word that is not used, the count of possible combinations gets reduced by 17576. -- K Sathyadev, sathya2008k@gmail.com
The first alphabet is particular, for any one year. In the next set, three-digit combinations can be formed in 10*10*10 = 1000 ways. In the next set, three-alphabet-combinations can be formed in 26*26*26 = 17576 ways. Hence the maximum number of vehicles that can be licensed in a particular year is 17576000. Corresponding to any combination of three letters, there are a thousand possible combinations of the digits. So the theoretical maximum is reduced by 1000. -- Ashwini Kumar Acharya, akacharya1234@gmail.com
(The second one was: “You have a 3-inch cube that you want to cut into 27 1-inch cubes. This can be done by making six cuts. Can it be done with fewer cuts by rearranging the pieces between cuts?”)
The 12 edge cubes have 4 interior faces; the six face cubes have 5 interior faces and the one centre cube has all the 6 faces as interior. Under no circumstances can a single cut expose more than one face of a sub-block. So if we focus on that cube we can conclude that six cuts will be required to expose all its faces. -- Saishankar Swaminathan, saishankar482@gmail.com
The answer is NO. It is not possible to cut the 3” cube into 27 identical cubes with fewer than six cuts, for the simple reason that the innermost cube has to be formed with six separate cuts to give it the required six-faced shape. -- Saifuddin S F Khomosi, Dubai.
(The third problem was about why simulator type screen projections couldn’t be used for actual aircraft landings in low or degraded visibility when pilots have a problem.)
The recorded landing cannot be just followed on all occasions because though the topographic conditions of airport are same, the other variables like wind direction and speed, snow condition resulting in variation of tyre friction and, lastly, other air traffic are not factored in. All these play a role in landing requiring a pilot’s real time control. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com
During landings, Qantas provides the facility of linking their aircraft’s Instrument Landing System with their passengers’ virtual reality goggles thereby using technology to connect with their customers. -- Shashi Shekher Thakur, shashishekher@yahoo.com
BUT GOOGLE THIS NOW
1. Here’s another old one: how many pets do you have if all of them are camels except two, all are giraffes except two, and all of them are llamas except two? The trick is you also have to give two answers.
2. There are two one-hour fuses. Meaning, after being lit they burn out in exactly one hour. But they burn very unevenly during that hour -- sometimes faster, sometimes slower. Given a matchbox, how can one measure 45 minutes?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)