Here’s the deal. We are a grand total of nine over or underpaid workers in a sweatshop and for no particular rhyme or reason one bright fine morning in July we all want to discover what our average salary might be. But there’s a teensy weensy bit of a mega hassle. In short, no one amongst us wants to disclose to the others how much he or she is being paid. Me , being too clever by half for my own good, have found a way to get that average without knowing anyone’s remuneration. Can you be cleverer by half than me?
THROUGHPUT
(Ye olde conundrum was about a biased coin and how using a combination of two coin tosses instead of one, can you find a way of making the random decision fair?)
The coin can still be used for fair results. In tossing the coin twice; if the results match, start over, forgetting both results. If the results differ, use the first result, forgetting the second. The reason is that the probability of getting heads and then tails must be the same as the probability of getting tails and then heads; as the coin is not changing its bias between tosses and the two tosses are independent. -- Saifuddin S F Khomosi, Dubai.
The four outcomes (HH, HT, TH, TT) on flipping the biased coin twice have probability 0.5625, 0.1875, 0.1875, and 0.0625. So we can pick the first movie if the outcome of the trial is HT, and the second movie if the outcome is TH. This is because both these outcomes have equal probability. -- Badri Toppur, badri.toppur@gmail.com
(The second one was about the last instalment of the two missing letters of yore.)
AFTER in capitals is a dead giveaway. So the missing letters are N & U. To should elaborate: while A & R are missing letters in the initial problem, the letters N U from the list are missing in AFTER. – A V Ramana Rao, raoavr@gmail.com (No, sorry. – MS)
This is about the eight planets and the second question after the first question. The missing letters are nothing but the first and last letters of the planet after removing the second and second last letters : A and R. Thus the remaining letters are M and S, isn’t that right MS? -- Dhruv Narayan, dhruv510@gmail.com (It is! – MS)
The third problem was: “The meaning of a common English word becomes its own plural when an A is added in front. What is the word?”)
I have it -- rather the AYES have it -- the AYES have it, the AYES have it.
YES is the word that transforms into AYES. -- Ajit Athle, ajitathle@gmail.com
The plural of the common English word is: PLENTY/APLENTY. -- Suseelan Padmanabhan, suseelanp@gmail.com
The word PACE means a single step in walking or running. On adding A in front, it becomes APACE which means to move swiftly which is equivalent to a number of paces. -- Narayana Murty Karri, k_n_murty@yahoo.com
(Here cone some over dated grouses and affirmations now.)
The spiral staircase problem (for which you published the solution last fortnight, the answer is correct, but I don’t know why Mr Nidugondi had to resort to such complex calculations. See, for every step you take, you gain 1 foot of altitude. So to gain 300 feet, you need 300 steps. It is that simple.. -- Prof S Manikutty, manikuti@iima.ac.in
The published answer shows the length of the staircase as 300.022 ft. The tower is 300 ft. high. It makes the staircase a vertical line instead of a spiral. The perimeter of the circular base of diameter 23 feet 10.5 inches is (pi)*23.875 = 75 feet. The published answer has taken each of the 4 turns as a circle. How do you climb from one circle to the other? Correct answer must be 424 feet meaning 424 steps. -- Abhay Prakash, abhayprakash@hotmail.com
BUT GOOGLE THIS NOW
1. LEFT, OFF, SCREEN, DUST, SEED, OUT, TRIM. What’s common to all of them?
2. If you placed a 6×6 cm square on a triangle, you could cover up to 60% of the triangle. If you place the triangle on the square, you can cover up to 2/3 of the square. What is the area, in square cms, of the triangle?
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)