A 3x3 grid contains the nine letters Q R S, T U V and W X Y. Now if each of them stands for one of the numbers 1 through 9 but no two letters stand for the same number, can you deduce the numbers represented by each letter if (a) in one of the two diagonals QUY or SUW the three numbers are all perfect squares; (b) either one of the diagonals or one of the rows consists of three consecutive numbers in some order; (c) Y is larger than T and both Y and T are evenly divisible by X which is not 1; (d) V + Q = R*W and (e) both T and U are evenly divisible by R which is not 1.
THROUGHPUT
(The sun-ripened tomato problem was about the statement: “When a spacecraft re-enters the Earth’s atmosphere its surface gets extremely hot due to friction with air particles.” And the question was why this was not a complete answer?)
Rockets have a heat shield when launched which is discarded once they reach the stratosphere. On the other hand, there is no protection at re-entry (Actually they do -- MS) -- Gadepalli Subrahmanyam, gsmani174@gmail.com
While ascending, spacecrafts do not move fast enough because they have just enough fuel to reach escape velocity and nothing more but while descending they are at the whims of gravity and go much faster, even when entering at an angle. This free fall fast movement due to gravity compresses the air in front of the spacecraft when it is re-entering. This, in turn, heats up the air molecules and can cause enormous damage. -- Shashi Shekher Thakur, shashishekher@yahoo.com
(The second was a reader variation of an earlier problem: “Today is a Monday; what day will it be after 23,999,997 hours, with all those complications of leap years and so on?”)
23999997 hours = 1000000 days minus 3 hours = 999999 days plus 23 hours = 142857 weeks plus 23 hours. So, the day will be a Tuesday. It is not necessary to take into consideration the leap years, etc, as we are calculating only the day and not the date. -- Dr P Gnanaseharan, gnanam.chithrabanu@gmail.com
23,999,997 hours is just short of 24,000,000 hours by 3 hours. The required day is 1 million days hence, but short by 3 hours. I million days has 142857 weeks and 1 day (1 million divided by 7). So if today is Monday, the required day is (1 day - 3 hours) from Monday. Therefore the exact day would depend upon what time it is on the starting Monday. For times between 0300 hrs to midnight, the answer is Tuesday. For times between 0000 hrs to 0300 hrs, the answer is Monday. Leap years, leap centuries do not matter as there are only seven days in a week. -- Dr Ramakrishna Easwaran, drrke12@gmail.com
(The last one concerned a spring balance, a rock A, the Moon, another rock B, an astronaut and for some unfathomable reason a pulley. And if that was not duhh enough, you then had to figure out the mass of stone B.)
I was really puzzled for quite some time by the puzzle. The input of gravitational force on moon given as 1/6 of gravitation on Earth and that rock B read 9.8 newtons on the moon the mass has to be 6 kg. Then why the second complex data? Newtonian thinking perhaps. Then I noticed the word “about” before 1/6. So it is more of reading between lines. So taking Earth’s gravitational acceleration as . . . blah blah blah . . . 5.745 kg should be the solution. It can also be found by trial and error. -- Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com
Let m1 and g1 be the unknown heavier mass & lunar acceleration respectively. Then from the given observations: ((m1 -1)/(m1 + 1))*g1 = 1.2, g1 = 9.8/m1. This gives us two possible answers: m1 = 1.421 kg and g1 = 6.894 m/s^2 or m1 = 5.745 kg and g1 = 1.706 m/s^2 of which only the latter is admissible since it is given that g1 is about g/6 or about 1.635 m/s^2. Seemingly simple but a nice problem that had me confused for a short while. -- Ajit Athle, ajitathle@gmail.com
BUT GOOGLE THIS NOW
1. See if you can figure out the four words from the following definitions: Dependent on chance; Like pheasants and domestic fowls; Cannibalism outside tribe or family; Person who is an expert in table talk.
2. If you can do the above, then the first letters of the four words make another word which backwards make a painter without an S.
Mukul Sharma
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)