What you have to do is evaluate each of the 10 following statements and say which is the only one amongst them which is true. It’s not easy.
(1) Exactly one statement on this list is false. (2) Exactly two statements on this list are false. (3) Exactly three statements on this list are false. (4) Exactly four statements on this list are false. (5) Exactly five statements on this list are false. (6) Exactly six statements on this list are false. (7) Exactly seven statements on this list are false. (8) Exactly eight statements on this list are false. (9) Exactly nine statements on this list are false. (10) Exactly ten statements on this list are false.
THROUGHPUT
(The question was: “I’ve written my name in 1 cm letters with a pen without any other help than my naked hands. I can make the letters grow and then make them decrease to their original size. Also, I can destroy the letters and rejoin them. Where did I write it? “
Come on, we all did this in school! Take a pen and write your name on the page-edge side of a book. Now you can enlarge it by fluffing the page-edge out and you can destroy the writing by simply opening out the book at any page without destroying the writing because when you close the book, there it is. -- Dhruv Narayan, dhruv510@gmail.com
I have written my name on a computer screen with a pen in-built in the computer, with only my naked hands using a keyboard. I can make the letters grow (but not the material on which they are written) in size or reduce them to their original size without affecting the screen. I can also make the letters disappear without affecting the screen. I can destroy the letters and rejoin them without using any adhesive substance. -- Narayana Murty Karri, k_n_murty@yahoo.com
(The second one was: “If you’re allowed to climb either one or two steps at a time, what are the total number of ways you can ascend a flight of 14 steps?”)
There are 610 possible ways of doing this. One step at a time; two steps at a time: 1. Other possibilities are as follows: Two 1 steps + Six 2 steps giving 8!/6!2! = 28 ways. Four 1 steps + five 2 steps giving 9!/4!5! = 126 ways. Six 1 steps + four 2 steps giving 10!/6!4! = 210 ways. Eight 1 steps + three 2 steps giving 11!/8!3! = 165 ways. Ten 1 steps + two 2 steps giving 12!/10!2! = 66 ways. Twelve 1 steps + one 2 steps giving 13!/12!1! = 13 ways. Therefore the total number of ways is, 1 + 1 + 28 + 126 + 165 + 66 + 13 = 610 ways. -- Gopu Natarajan, natarajangopunatarajan3@gmail.com
Going one or two steps at a time I can climb the steps in 610 ways. This question can be solved by dividing the problem into different cases. Case 1: when all steps are ascended one at a time -- 1 way; case 2: all steps are ascended two at a time -- 1 way; case 3: two 1 steps and six 2 steps -- this can be done using the permutation formula and using this we get 28 ways. Similarly we can do the same for all subsequent cases and adding them gives us the answer as 610. -- Akshit Chaturvedi, akshit0201@gmail.com
(The third problem was: “Why is it that tea leaves at the bottom of a glass or cup (which means that they’re heavier than water) don’t move towards the walls under the influence of centrifugal force when stirred but assemble at the centre of the bottom?”)
In a teacup, where the rotation is slower at the bottom, the pressure gradient takes over and creates an inward flow along the bottom. Higher up, the liquid flows outward instead. This secondary flow travels inward along the bottom bringing the leaves to the centre, then up, out and down near the rim. The leaves are too heavy to lift upwards, so they stay in the middle. Combined with the primary rotational flow, the leaves will spiral inward along the bottom. -- U N Murthy, u_n_murthy@rediffmail.com
When stirred, the water starts to circle and gets thrown to the outer side of the circle and moves faster than at the middle due to centrifugal force. It becomes higher nearer the outside creating pressure gradient from outside to the middle and very little at the centre of the bottom. It forms a vortex. The pressure gradient pulls the leaves (which are heavier than water) to the centre of the bottom. -- Abhay Prakash, abhayprakash@hotmail.com
BUT GOOGLE THIS NOW
1. You can walk across a bridge in 10 minutes. But a guard in a room at one end won’t let you cross. However, he stays inside for five minutes and then comes out to inspect for five minutes. If he catches you, he forces you to go back. So how do you go across?
2. What are the next two numbers in the series 202, 122, 232, 425, 262, 728, ?, ?.
Sharma is a scriptwriter and former editor of Science Today magazine.(mukul.mindsport@gmail.com)