Here’s the thing. There are two new movies playing in town, one starring Scarlett Johansson and the other Johnny Depp. Now obviously the male in you wants to ogle the Ett while your female side wants to drool the Epp. So instead of going to a shrink to sort out your messed up head you decide to flip a coin.
But the hassle is, you have only one coin and it’s biased. Meaning, heads comes up with a probability of 0.75 instead of 0.5 as in any normal small change that usually rattles around in your pocket. However being very just you want both facets of your crazy mixed up psyche to have a fair chance of getting to eyeball who they want. Using a combination of two coin tosses instead of one, can you find a way of making the random decision fair?
THROUGHPUT
(Here’s a summary of a summary I had given of the problem: 300 feet high tower; handrail of spiral steps circles it four times; balusters, one to each step, one foot apart; dia of spiral steps cylinder 23’ 10.5”. How many steps to the top of the tower?)
Assuming the distance between balusters is measured along the perimeter of the staircase, the number of steps can be calculated by dividing the staircase perimeter by distance between balusters (1 foot). Staircase perimeter (4*pi*diameter) comes to about 300 ft (300.022.ft). So number of steps comes to 300. Note: The perimeter is the projected perimeter of four circles when looked from top and not length of the spiral. -- Ravi Nidugondi, ravi.nidugondi@gmail.com
(The second one was: “A number ends with the digit 2. If we move this 2 from the last place to the first, the new number is twice the original. What’s the number?”)
The number we are looking for is 105,263,157,894,736,842. I derived it by writing an equation: 2a/2 = a2 (assuming the number to be two-digit). We find that whatever value ‘a’ possesses, the last digit on the LHS will be 4. So, we can rearrange the equation as: 2a42 = a42. Here we see that whatever value ‘a’ possesses, the second-last digit on the LHS will be 8. Rearranging again, we get 2a84/2 = a842 (note again that irrespective of value of ‘a’, the third-last digit on LHS is 6). So . . . blah blah blah. -- Saifuddin S F Khomosi, Dubai.
The answer is, well hold your breath, 105, 263, 157, 894, 736, 842. You mean this is easy? Tried first with 2 or 3 or 4 digits at random and failed. Tried systematic multiplication and lost patience and ran out of paper after reaching an 8-digit number. Then tried algebra and ended up with something that was way above me. Finally turned to Google and reached this wonderful video. Watch “What Positive Number Doubles When The Last Digit Moves To The First Digit? Riddle For “Geniuses”’’. -- Dr. Ramakrishna Easwaran drrke12@gmail.com
(Among the first five who also got it right are: Thamban Nair.M, tham.nair@gmail.com; Narasimha Murthy Uppu, u_n_murthy@yahoo.com; Hemalatha T, hemalatha1956@gmail.com; Raghavendra Rao Hebbani, rao.raghavendrah@gmail.com; Ramesh Kumar, rameshkumarthayyil@gmail.com.)
(The third problem was: “We all know how to get the error symbol ‘E’ on a calculator. Now the question is, how will you get two such symbols consecutively as ‘EE’?”)
The symbol EE is a scientific notation and it stands for “Engineering Exponent” or “Enter Exponent”. It actually means “times 10 to the power of that I enter next”. For example, 5 EE 8 = 5x(10)^8. However, one has to be careful when entering a negative exponent. For example, for 5x(10)^(- 3), if we press 5 EE -3 on the calculator, the calculator may perform the operation 5x(10)^0 -3 = 5 - 3 = 2. Instead, one must use the ‘change sign’ key.
And check the display to see if the exponent is correctly taken or not. -- Narayana Murty Karri, k_n_murty@yahoo.com
Yes, it’s easy to get an E on a calculator. As for getting two Es, the only way I could think of, is to type 33 and turn the calculator upside down. Now, does that count? -- Balagopalan Nair K, balagopalannair@gmail.com
BUT GOOGLE THIS NOW
1. What three digits are represented by X, Y, and Z in this addition problem? XZY + XYZ = YZX?
2. What is the only temperature that is a prime in both Celsius and Fahrenheit?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)