# Tagged Questions

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### Homework Question for a 15 year old

My younger brother(age: 14 years 7 months) and his classmates were given a set of eight questions by his class-teacher, which included the following two questions: (i) Find, if you can, the fallacy ...
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### Arrangement of Numbers to Get a Common Sum

I'm having trouble with a math problem. I need to arrange 6 numbers on a certain diagram: At every intersection of two circles, I have to put one of these six numbers: 4, 5, 5, 6, 6, or 7. The sum ...
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### Find Differences between Ages of A and B.

Question: A says to B, I am twice as old as you were, when I was as old as you are. If the sum of ages is 63 years. Find the difference between their ages. My Question: I understand that we need to ...
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### What is the subset of the letters in the word 'numbers'

What is the subset of the letters in 'numbers'? I thought it meant to make a word out of the letters in 'numbers' so I tried to make a word out of it, but I couldn't make a word and so I don't ...
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### Josephus Variant

I set myself the challenge of trying to solve a variant of trying to solve a variant of the josephus problem where instead of killing every second person, every third person dies. The formula for the ...
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### How to prove that in optimal strategie of tower of Hanoi none of the disks can't be placed on a disk of same parity

How to prove that in optimal strategie of tower of Hanoi none of the disks can't be placed on a disk of same parity if we have 3 rods. So for example disk 2 can't be placed on disk 4, or disk 1 can't ...
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### How many triangle can be drawn with those points? [duplicate]

There are 7 points on the circumference of a circle.How many acute triangle can be drawn with those points. please help me to solve this problem.
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### Come up with some fun “equation Limericks”

We were discussing "Limericks" in my Calculus class. Specifically, "equation Limericks". A Limerick is a poem with five lines. The first, second, and fifth lines should have nine syllables each and ...
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### If $x^3+\frac1{x^2}=1$, what is $x^3+\frac1{x^3}$?

$x^3 + \frac1{x^2} = 1$. Then, $x^3 + \frac1{x^3} = ~?$ $p + \frac1{p^2} = 47$. Then, $p + \frac1p = ~?$
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### What is the most mathematical flag?

I know it sounds stupid. But my professor asked us which is the most mathematical flag. As I know most of the flags of the countries are rectangle then what does he mean by most mathematical flag?
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### Coded language puzzle!! [closed]

Here is a puzzle I can't crack. It goes like this: In a certain coded language MANGO=3/5 ORANGE=2/6 APPLE=1/5 Then, POTATO=?? The answer is 5/6. I would like to know to arrive at the answer.
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I stumbled upon a puzzle I can't crack. It goes like this: In a certain Code language: 7321=6 5342=3 8645=15 Then 9312=? The Answer is 9. But I can't seem to find the logic behind it??
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### Don't understand this problem: There are only 2 pairs of positive integers $(x,y)$ for which…

..both $\frac{21}{x}$ and $\frac{70}{y}$ are in lowest terms and for which $\frac{21}{x} + \frac{70}{y}$ is an integer. One such pair is $(1,1)$. What is the other such pair? This is a Mathematics ...
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### Linear Transformation Brief Question

$T:P_{3}\rightarrow P_{3}$ defined by $T(p(t))=tp'(t)+p(0)$ is a linear transformation. Determine whether $T$ is invertible. If yes, find $T^{-1}(q(t))$, where $q(t)$ is a polynomial of degree at ...
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### How many $n$-disk legal configurations are there for the Tower of Hanoi?

This question comes from this homework assignment from ECS20 at UC Davis. How many $n$-disk legal configurations are there for the Tower of Hanoi? A "legal configuration" means that no disk is ...
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### Linear algebra function that creates decreasing product vector of original vector

For vector $y=[y_1,y_2,\dots y_n]$ , let $\gamma = \sum_{i=1}^n \gamma_i$ , and $\gamma_i(n-i+1)=y_n*y_{n-1}*\dots y_i$ so that $\gamma$ looks like $[y_1*y_2*\dots y_n, y_2*\dots*y_{n}, \dots y_n]$ ...
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### What is the Probability that a Knight stays on chessboard after N hops?

Say a $8 \times 8$ chessboard as per picture. A position is represented here by co-ordinates $(x,y)$. A move is aslo considered as valid, where the Knight lands outside the chessboard [ For eg. ...
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### function with restrictions in finding solutions

Please help... How to prove the following functional equation, which has no solution. $A + B + C + (A + B)C - 2 = 0$ has no solution, where $A = f(x)$, $B = g(x)$ and $C = h(x)$. Here $A, B$ and $C$ ...
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### $\square\square\times\square =\square\square\square =\square\times\square\square\,\,\,$ fill blanks with distinct numbers from$\{1,2,3,4,5,6,7,8,9\}$

Fill in the blanks of: $$\square \;\square \times \square = \square \; \square \;\square =\square \times \square \;\square$$ With distinct numbers from the set $\{1,2,3,4,5,6,7,8,9\}$. I was ...
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### How Many Clock Hand Positions Swap to a Valid Position?

My wording will not be exactly clear, but this is what I remember. Suppose you have a clock with minute and hour hands and you switch their places to form another correct time. How many such times ...
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### Minimum number of coconuts

Three friends namely $A$, $B$ and $C$ collected coconuts with the help of monkey and fell asleep. At night, $A$ woke up and decided to have his share. He divided coconuts into three shares, gave the ...
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### When will two cars pass each other

There was a question in my math text book the other day that stated: $2$ cars each travelling at a constant velocity around a ring , complete exactly $4$ and $7$ rounds in one hour. If they start at ...
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### Interesting and irritating problem.

How to deal this problem. I found this problem in math competation in 2012. But, I could not solve. Could you help me... Uncle John has taken blood pressure drops for a long time according to the ...
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### In how many ways ( using only whole numbers ) can we divide 49 into 6 parts so that we can obtain any number between 1 to 49?

The series which forms the basis of all the other series is:- 1,2,4,8,16,18. Some other combinations are:- 1,2,3,7,14,22 ; 1,2,4,7,15,20 ; 1,2,4,8,13,21. However, I obtained the basic combination by ...
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### 100 roads in a city, 1 is closed

In a certain country, 100 roads lead out of each city, and one can travel along those roads from any city to any other. One road is closed for repairs. Prove that one can still get from any city to ...
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### using numbers 1 to 9 only once to equal 1 million

Using digits 1,2,3,4,5,6,7,8,9 only once how do you equal 1 million. Adding, multiplication, subtraction and division
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### Logic puzzle about travel times and distances

Each of the four person – Pawan, Rahul , SGR, Ankit –travelled at a different uniform speed out of 10 km/hr, 15 km/hr,20km/hr, and 25 km/hr for different time durations- 30 hours, 40 hours, 50 hours ...
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### Diagramatic Puzzle

This is the Puzzle: and this is the hint: and the answer seems to be 000111 but I have absolutely no idea how it is done. Can anyonw help me out here? That's the puzzle. There are no other ...
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### Mental math tip needed; moving decimal around on larger and smaller numbers?

When I do calculations I like to round off to say nanometers for wavelength. That means I need it in the form $whatever \times 10^{-9}$. The problem here is that regardless of the number I manage to ...
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### Combinations of a penny, nickle, dime, and quarter

You have one penny, one nickle, one dime, and one quarter. How many different amounts of money can you make using one or more of these coins? Please help me! I'm having trouble! Im having trouble I ...
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### Solving an inequality, the equality is facing the wrong way?

I'm suppose to solve a problem that goes like this. The graph for the following function f given by $f(x) = 115.82 \cdot 0.94^x + 5$, with $x \geq 5$, gives the temperature of the water after ...
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### Probability, why my solution doesn't work out? (P of drawing a pair)

The task is simple, the probability of drawing a pair of cards. You draw two cards from a stack, what is the chance that you get two kings or two fours. My idea was the following. There are 13 ...
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### Drawing three cards of different type

I did draw a tree and found out that this can be done in 24 different ways. But is there a quicker formula? There are a total of four different types of cards, as you know. And we are to draw three of ...
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### Eight queens problem, wondering about the non-unique solutions

I've done the code that generates all the solutions. But know I am suppose to filter out any redundant solutions based on symmetry and rotations. I have code for vertical symmetry, horizontal ...
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### Proof for divisibility rule for palindromic integers

I am studying for a test and came across this in my practice materials. I can prove it simply for some individual cases, but I don't know where to start to prove the full statement. Can you help me? ...
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### The Game of Nim

A position in Nim consists of some piles of coins. Two players alternate, with each move removing a portion of one pile. The winner is the player who takes the last coin. Suppose that the starting ...