When I was younger (though actually I was much older) I used to wonder what would happen if I stood on a weighing scale while gravitationally free falling. Yes, I know it would register no weight, but what if I were to hold another identical scale over my head and pull it down with my hands? Yes, it would only register my muscle’s pull power. But now that I’m older (though actually I’m much younger) I now wonder what if I could hunker down and pull the head scale with one hand and the foot one with the other? Would it show my true weight?
If not, then a chain of length L cm and mass M kg is suspended vertically by one end with the other end immediately above a scale. The chain is released and falls. At the instant the entire chain has fallen onto the scale what does the scale read?
THROUGHPUT
(The problem was about the message MERRY XMAS TO ALL which was sent in coded form by a math prof to all his friends by replacing all the letters with digits. Blah blah blah and stuff and then there were two answers, to be derived.)
The message was: 185^, 86^2, 9^2, 30^2 . It expands to 34225, 7396, 81, 900. 0 stands for L, 1 for O, 2 for R, 3 for M, 4 for E, 5 for Y, 6 for S, 7 for X, 8 for T and 9 for A.
Fixing X as 7 and the double letters L in ALL and R in MERRY helped. -- J Vaseekhar Manuel, orcontactme@gmail.com (Hey JVM: TWO answers remember? -- MS)
Since ALL is a perfect square, there are only three numbers which foot the bill: 144, 400 & 900 and since in XMAS, A occurs in third place, list out all the four digit squares which have either 1, 4 or 9 in third place and with other digits being different and we find the numbers 1296, 1849, 2916 , 3249, 4096, 5041, 6241, 7396, 8649 & 9216 which meet the requirement. And since MERRY is a perfect square, it is easy to find five digit number squares which have same digit in third and fourth places and with other three digits being different. And there are not many of them. Now it is easy to infer that M has to be either 2, 3 or 6 and substituting striking out we get two sets of solutions: 27556 3249 81 400 and 34225 7396 81 900. -- A V Ramana Rao, raoavr@gmail.com
Answer 1: The letters A, E, L, M, O, R, S, T, X, Y represent the digits 4, 7, 0, 2, 1, 5, 9, 8, 3, 6 respectively so that the message is transformed as 27556 3249 81 400, where each of the four numbers is a perfect square. Answer 2: The letters A, E, L, M, O, R, S, T, X, Y represent the digits 9, 4, 0, 3, 1, 2, 6, 8, 7, 5 respectively so that the message is transformed as 34225 7396 81 900, where each of the four numbers is a perfect square. -- K Narayana Murty, k_n_murty@yahoo.com
(The other problem was: “You must have noticed that sometimes some clothes like thick cottons acquire a shininess when they’re ironed. What is this due to?”)
I think because of the heat of the iron transferred to the cloth, the cloth surface radiates or reflects more light giving the impression as if it is shining. The shining may not be there after the cloth cools down. -- Narasimha Murthy Uppu, u_n_murthy@yahoo.com
This is because the water molecules in the micropores of cotton fabric available in ionic state are attached to the pigments of the fabric..After hot pressing the fabric the same water with ionic pigments attachment oozes out to the surface of the fabric increasing its shininess. -- Nrusingha Behera, ncb123.age@gmail.com
(Nope, nobody got it right. It’s because with thick cottons we generally tend to overheat the irons while pressing. The result is the top layer of the material gets partially melted and runs together to form a smooth reflective surface. Ordinarily, when viewed under magnification, this surface layer of fibres is rough and does not reflect light and therefore the sheen is not there. To avoid getting the shine, pressers usually put an intervening layer of some other cloth in order to avoid direct contact with the iron.)
BUT GOOGLE THIS NOW
1. Can you replace the “?” with the correct three letters? voN luJ ? raM beF.
2. When Raja was six years old he made an indelible ink mark on his backyard tree to indicate his height. Five years later at age eleven, he returned to see how much higher the mark was. If the tree grew by 7.5 cms every quarter, how much higher would the mark be?