Let’s say you’re driving in your fancy stretch limo to a particular destination, wherever the heck that is. The only assumption is that you’re free to drive at any speed you choose (I mean it’s your car for the love of Mike) with no traffic jams or cops out on the take to nab you. For the first half of the journey (and by half I mean half the overall distance between the starting point and your finishing point) you drive at 20 kilometres per hour.
You then realise that it’s all taking way, way much too long, and that you’re going to be majorly late for your serious and favourite mob meeting. You therefore decide that you’re going to increase your speed so that your overall average speed for the whole journey will be 40 kilometres per hour. How fast do you have to drive for the remaining part of your journey in order for your average speed for the whole journey to be 40 kmph? (Incidentally and strangely enough the answer’s the same, whatever the total distance of your journey.)
THROUGHPUT
(The overbaked problem of yesterweek was: “A PEAR, an APPLE, a LEMON and a BANANA all add up to an ORANGE. If each letter represents a number between 0 and 9 -- both inclusive -- solve the equation.”).
The answer to PEAR + APPLE + LEMON + BANANA = ORANGE is 9782 + 89947 + 47530 + 180808 = 328067. It was a tough one even by Googling standards and required sheer force. Phew! -- Charanjit Singh Pardesi, cspardesi@gmail.com.
This can be solved by using a computer running C language. After compiling and running the program, the computer solves the equation denoted by the letters to allocate a corresponding number to the numeric variables that reads as N = 0, B = 1, R = 2, O = 3, L = 4, M = 5, G = 6, E = 7, A = 8 and P = 9. The numeric equation then transforms into 9782 (PEAR) + 89947 (APPLE) + 47530 (LEMON) + 180808 (BANANA) = 328067 (ORANGE) thereby solving the riddle. -- Shashi Shekher Thakur, shashishekher@yahoo.com.
(The second half-baked one was: “Okay so you’ve managed to get that peeled hardboiled egg into a wide-ish necked bottle. How do you get it out now without breaking the bottle? Two answers are preferable but even one will do.”)
One of the best methods to remove an egg from a bottle is to tilt the bottle such that the egg comes to the opening and then to blow air inside the bottle with your mouth. This causes air pressure behind the egg to rise and eventually the egg comes out. -- ReubenRomal Thomas, reubenromal123@gmail.com
Another method would be to apply oil to the inside of the mouth of the bottle, hold it upside down in one hand and bring it down smartly across your other arm (much like handing a bottle of thick ketchup which refuses to budge in the normal way). -- Kishore Rao, kishoremrao@hotmail.com.
The egg can be taken out by increasing the pressure inside the bottle in two ways: (1) invert the bottle; now the egg will be at the neck and just closing it. Then heat the top end of the bottle and the egg will come out pushed by the hot air inside. (2) Hold the bottle horizontally and blow air strongly into the bottle and quickly tilt it slightly so that the egg just closes the opening and watch it comes out of the bottle. -- Ramesh Kumar, rameshkumarthayyil@gmail.com.
(The unbaked third problem was to get an unpeeled hardboiled egg into a similarly necked bottle without breaking the shell -- plus how to get the contents of an egg out without breaking the shell.)
First soak the egg in vinegar which softens the shell. Then light a taper inside the bottle and take the vinegar-soaked egg and put it on the top of the bottle. The fire can’t live without any oxygen so it will try to suck it from the entrance. When the fire does this it sucks the egg into the bottle. -- Narayana Murty Karri, k_n_murty@yahoo.com.
Simply put it under a hen. The contents (young chick) will break the shell when it is ready to come out! -- Dhruv Narayan, dhruv510@gmail.com
BUT GOOGLE THIS NOW
1. How can you show that in any year the same days of the month in March and November fall on the same day of the week?
2. A slice of uniform thickness of one centimetre is cut from a sphere of diameter 10 centimetres. What is the curved area of the slice?
— Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)