10 Fun puzzles to enjoy today

1st April is a day of fun, humor and enjoyment. Even though, I have lot of fun puzzles on this blog, these ten are totally meant for today. Enjoy! PUZZLES 1. If you are in a dark room with a candle, a wood stove and a gas lamp. You only have one matchstick in the matchbox, so what do you light first? 2. If the question you answered before you answered the question you answered after you answered the question you answered…

Difference Paradox

Consider two natural numbers $n_1$ and $n_2$, out of which one is twice as large as the other. We are not told whether $n_1$ is larger or $n_2$, we can state following two propositions: PROPOSITION 1: The difference $n_1-n_2$, if $n_1 >n_2$, is different from the difference $n_2-n_1$, if $n_2 >n_1$. PROPOSITION 2: The difference $n_1-n_2$, if $n_1 >n_2$, is the same as the difference $n_2-n_1$, if $n_2 >n_1$. Moving on the proofs: PROOF OF PROPOSITION 1: Let $n_1 > n_2$, then $n_1=2n_2$.…

What’s The Question Aladin

What’s the question, if the answer is ‘No!’

Infinitely many answers questions are possible to the answer, "No". So, our real task should be to find one of THOSE many, which seems to be a perfect one. A simple and the first ever logical approach of giving answers to a question is to derive answers from the question, that is, replace some words of the question with reasonable ones and make a statement. (Conversely but ) Similarly, we can try to derive the questions from the given answer.   So,…

Light the bulb: An everyday logic puzzle

You are inside a room and there are exactly three electric bulbs outside of the room. The three bulbs have their corresponding switches (exactly three) inside the room. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which electric bulb, if you are allowed to go outside and come inside the room only once? This is a logic puzzle, which was asked to me by a friend…

Smart Fallacies: i=1, 1= 2 and 1= 3

This mathematical fallacy is due to a simple assumption, that $ -1=\dfrac{-1}{1}=\dfrac{1}{-1}$ . Proceeding with $ \dfrac{-1}{1}=\dfrac{1}{-1}$ and taking square-roots of both sides, we get: $ \dfrac{\sqrt{-1}}{\sqrt{1}}=\dfrac{\sqrt{1}}{\sqrt{-1}}$ Now, as the Euler's constant $ i= \sqrt{-1}$ and $ \sqrt{1}=1$ , we can have $ \dfrac{i}{1}=\dfrac{1}{i} \ldots \{1 \}$ $ \Rightarrow i^2=1 \ldots \{2 \}$ . This is complete contradiction to the fact that $ i^2=-1$ . Again, as $ \dfrac{i}{1}=\dfrac{1}{i}$ or, $ i^2=1$ or, $ i^2+2=1+2$ or, $ -1+2=3$ $ 1=3…

Four way valid expression

People really like to twist the numbers and digits bringing fun into life. For example, someone asks, "how much is two and two?" : the answer should be four according to basic (decimal based) arithmetic. But the same  with base three (in ternary number system) equals to 11. Two and Two also equals to Twenty Two. Similarly there are many ways you can add them and get different results. Dmitri A. Borgmann, the German recreationalist, puzzler and father of logology, noticed the following expression…

How Many Fishes in One Year? [A Puzzle in Making]

This is a puzzle which I told to my classmates during a talk, a few days before. I did not represent it as a puzzle, but a talk suggesting the importance of Math in general life. This is partially solved for me and I hope you will run your brain-horse to help me solve it completely. If you didn't notice, this puzzle is not a part of A Trip To Mathematics series. Puzzle which I discussed in the talk was…

The Cattle Problem

This is a famous problem of intermediate analysis, also known as 'Archimedes' Cattle Problem Puzzle', sent by Archimedes to Eratosthenes as a challenge to Alexandrian scholars. In it one is required to find the number of bulls and cows of each of four colors, the eight unknown quantities being connected by nine conditions. These conditions ultimately form a Pell equation which solution is necessary in case of finding the answer of the puzzle. The Greek puzzle is stated below with…

Yes No Puzzle

A Yes No Puzzle

This is not just math, but a very good test for linguistic reasoning. If you are serious about this test and think that you’ve a sharp [at least average] brain then read the statement (only) below –summarize it –find the conclusion and then answer that whether summary of the statement is Yes or No. [And if you’re not serious about the test …then read the whole post to know what the stupid author was trying to tell you. :-) ]…

Three Children, Two Friends and One Mathematical Puzzle

Two close friends, Robert and Thomas, met again after a gap of several years. Robert Said: I am now married and have three children. Thomas Said: That's great! How old they are? Robert: Thomas! Guess it yourself with some clues provided by me. The product of the ages of my children is 36. Thomas: Hmm... Not so helpful clue. Can you please give one more? Robert: Yeah! Can you see the number on the house across the street? Thomas: Yes!…

How Genius You Are

How Genius You Are?

Let have a Test: You need to make a calculation. Please do neither use a calculator nor a paper. Calculate everything "in your brain". Take 1000 and add 40. Now, add another 1000. Now add 30. Now, add 1000 again. Add 20. And add 1000 again. And an additional 10.   So, You Got The RESULT!  Quicker you see the answer, sharper you are! Did you think the result is 5000? Actually, it is not. The correct result is 4100.

A Problem On Several Triangles

A triangle $ T $ is divided into smaller triangles such that any two of the smaller triangles either have no point in common, or have a vertex in common, or actually have an edge in common. Thus no two smaller triangles touch along part of an edge of them. For an illustration let me denote the three vertices of T by 1, 2 and 3. Now number each of the vertices of the small triangles by 1, 2, 3.…