3
votes
2answers
58 views

Construct numbers using digits $123456789$ and the operations $+,-,×,÷$

From an old book I found the following question. Use the digits $1,2,3,4,5,6,7,8,9$ and the operations $"+,-,×,÷"$ with $( )$ for construct the result $100.$ During the computations the order of ...
2
votes
1answer
63 views

Mathematics of paper fold-cutting

Take a square of paper... ... and fold it any number of times using consecutive straight folds... ... then cut off any number of pieces using consecutive straight cuts... ... and unfold the ...
19
votes
10answers
3k views

Get $5$ by doing any operations with four $7$s

How can one combine four sevens with elementary operations to get $5$? For example $$\dfrac{(7+7)\times7}{7}$$ (though that does not equal $5$). I am not able to do this. Can you solve it or prove ...
0
votes
1answer
76 views

I'm not understanding this puzzle [closed]

At first, I was thinking, mininmum amount of sticks it takes to create the figure, and then how many draw strokes it takes to create the boxes without crossing paths...but I can't figure out what's ...
0
votes
3answers
122 views

Blue Eyes: A Logic Puzzle, has a puzzling solution (a.k.a. What does common knowledge have to do with it?)

In Blue eyes: a logic puzzle (specifically, the follow up questions), the most common answer is that it needs to be common knowledge that someone has blue eyes for all the blue-eyed people to leave. ...
1
vote
1answer
43 views

Why does the filling up of odd order magic square with numbers follow the knight movement?

Why does the filling up of odd order magic square with numbers follow the knight movement? I was reading about magic square, where I came up with the knight movement filling up of the magic square ...
0
votes
1answer
86 views

2048 algorithm for merging

Ok, here's a question my friend just sent me, ive mastered it to some extent, but am failing, so, please help a little: Your target is to merge these blocks in such a way that one bigger number is ...
1
vote
2answers
58 views

maximum number of independent bishops on a nxn chessboard

So I came across this problem where we have to find the maximum number of independent bishops on a nxn chessboard such that no two bishops attack each other . So after drawing the cases for $3$x$3$ , ...
16
votes
2answers
2k views

Interview puzzle with a deck of cards, some cards upside-down

You are sitting in a dark room. It is completely dark. You can't see anything and there is no way that you can make light. Basically, just assume that you are blind for this task. There is a table in ...
2
votes
1answer
69 views

How much distance did messenger cover? [closed]

A column of troops $80$m long is moving along a straight road at a uniform pace. A messenger is sent from the head of the column, delivers a message at the rear of the column and returns. He also ...
2
votes
2answers
336 views

Pirates And Coins No.1

I actually like this one: There are five pirates in a ship and they have found 100 coins. The biggest pirate offers a way to divide the coins. If at least half of them agree on the division, it will ...
3
votes
0answers
70 views

A game on a smaller graph

In this question Alice and Bob play a game on $K_{2014}$, Alice directing one edge, Bob directing $1$ to $1000$ edges with Alice trying to make a cycle. The proof that Alice can win depended on the ...
1
vote
1answer
148 views

logic\math question [closed]

Hi, This is allegedly a very simple question....most of the people answered that the answer is 9=90. i claim that theoretically, you can't be 100% sure about the right answer because you don't know ...
1
vote
1answer
62 views

Largest factor of sum of all 3-digit numbers…

What is the largest number (so, yes, I am looking for a discrete integer not an algebraic expression) by which the sum of all 3-digit numbers formed with the non-zero, distinct digits a, b, and c MUST ...
3
votes
1answer
140 views

When to be sure that we have counted all the squares in such problems [duplicate]

My first question is: How would one solve such problems (in general,squares+rectangles). What should be the general technique?How can this problem be reduced to a mathematical problem? My second ...
1
vote
1answer
80 views

Math Puzzle Solving

Using each of the digits 1,2,3,4,5,6,7,8 exactly once fill in the boxes so that no consecutive number is adjacent or cross to ...
2
votes
1answer
36 views

maximize the sum of numbers such that all of them are coprime

Suppose we have numbers from $2$ to $n$ (inclusive). We want to choose numbers such that all of them are coprime and give the maximum sum. For example, if $n=10$, then we choose $9,8,7,5$ and the ...
0
votes
0answers
39 views

writing a number as a sum of odd integers

How many ways are there of writing $n$ as a sum of odd integers, where the order doesn't matter? For example, there are $2$ ways of writing $3$: $(1,1,1)$ and $(3)$.
21
votes
2answers
344 views

The Plank Problem 2 Dimensions

We were trying to solve this wonderful problem, but have not succeeded to solve. It goes like this: Let $R=[0,1]^2$, and $D\subseteq R$ be a convex set which intersects each side of $R$. Define a ...
4
votes
2answers
116 views

expected value of a game with a n sided die

Suppose we have a n-sided die. When we roll it, we can be paid the outcome or we can choose to re-roll by paying $1/n$. What is the best strategy and what is the expected value of this game? As an ...
5
votes
1answer
137 views

Rooks in 3D chess board

How many rooks are needed for a 3D chess board of size NxNxN so that every empty cube on the board can be reached by a rook in a single move?
1
vote
2answers
103 views

hitting a dart board probability

You have a dart board which is split in half. If you hit the left half, you get $2$ points, if you hit the right half, you get $3$ points. You have an 80% chance of hitting the dart board on any ...
12
votes
4answers
628 views

expected value of a sum of a 10 sided die

Suppose you have a fair die with 10 sides with numbers from 1 to 10. You roll the die and take the sum until the sum is greater than 100. What is the expected value of this sum?
1
vote
1answer
40 views

counting of numbers

In a garden there are three kind of roses-red, yellow and white. No matter which 9 roses are selected at least 2 of them are white; and no matter which 10 roses are selected at least 2 of them are ...
1
vote
2answers
49 views

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 ...
0
votes
3answers
169 views

Probability that a leap year has 52 Sundays

For the Question "Find the probability that a leap year has 53 Sundays". The Solution goes : For 53 Sundays, we proceed as: $\frac{366}{7} = 52.28$; So we can be sure that there are 52 Sundays, ...
1
vote
3answers
70 views

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 ...
0
votes
1answer
67 views

Liar - Truth-Sayer - Tourist Problem. Construct the answer with the given 2 sub-statements.

A tourist A comes to a country where people are divided into two categories: Liars (L) and Truth Sayers (T). Ls always lie and Ts always speak the truth. Intending to walk to the capital, the tourist ...
0
votes
1answer
82 views

The famous Portia's casket problem

Gold casket: the portrait isn't in the silver casket. Silver: the portrait isn't in this casket. Lead: the portrait is in this casket. At least one of the statements was true and at least one of them ...
-1
votes
3answers
1k views

Tricky Question with multiple solutions but only one true answer [closed]

If 1112=25 1113=36 1114=47 1115=58 1117=? I came up with two solutions 80 and 710 Which would be the right answer?? there is no further hints and there is only one a single solution answer
1
vote
1answer
101 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
2
votes
0answers
93 views

Given a number of items, how many sets of three are there where no two sets are two thirds similar?

Sorry if the title isn't proper math-talk. Hopefully I can explain it better here. So let's say we have a set. 1, 2, 3, 4, 5, 6, 7, 8, 9. I want to know how many groups of three can be made where no ...
5
votes
1answer
151 views

Which mathematical game or puzzle did you invent?

A couple of weeks ago, a friend of mine showed me a extension of a game we are all familiar with that he was working on. The game we know is called Tic-Tac-Toe, and he was working on his own version ...
2
votes
2answers
116 views

Is there a solution to this Seating Plan problem?

So a colleague asked me for some Help on an interesting Problem, which we both couldn't find the optimal answer for. The event which needed it is already in the past, so this is just me trying to ...
0
votes
1answer
60 views

Calculate Income Of the Month [Puzzle]

Mr. Jill requires Rs 6000 per month to maintain his family. He saves 20% of any amount that he earns above Rs. 6000 but below Rs 7000 in a month. He saves 30% of amount that he earns above Rs 7000 but ...
1
vote
3answers
139 views

What is the next number? [closed]

What is the next number in the following set ? $$1,11,21,1211,111221, \ldots$$
-1
votes
1answer
102 views

Question on Speed and Distance

X, Y and Z move along a circular path of length 1.2 km with speeds of 6 km/h, 8 km/h and 9 km/h respectively. X and Y move in the same direction but Z moves in opposite direction. If they all start at ...
4
votes
1answer
94 views

General approach to puzzles such as the “6 books puzzle”

Six different books (A,B,C,D,E,F) of identical size are stacked as in the figure. We know A and D are not touching. E is between two books which are both vertical or both horizontal. C touches ...
3
votes
3answers
141 views

A puzzle that came when I am half awake

When I am about to wake up in the morning, a puzzle crept into my mind.It is when $\sqrt{a}$ and $\sqrt{b}$ are both non-integers where a,b are positive integers is it possible for $\sqrt{ab}$ to be ...
1
vote
2answers
72 views

Ball bouncing in a box, will it meet a vertex.

I have no idea upon how to solve this: A box 5cm by 3cm with a ball projected from a vertex at 45 degree angle, it reflexes at a 45 degree angle and keeps reflecting at a 45 degree angle. Will it ...
73
votes
12answers
8k views

Logic puzzle: Which octopus is telling the truth?

King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always tell the truth. One day, four servants met. ...
0
votes
1answer
602 views

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.
3
votes
0answers
168 views

Limits of infinite processes that terminate in finite time - checking my understanding?

I am a computer scientist by training, but have a fair amount of math background that I've picked up through classes, teaching, and general interest. A student of mine posed a question to me. I think ...
1
vote
2answers
170 views

Math Riddles #10 - Car Meter Riddle

Today my car meter reads as 72927 kms. I notes that this is a palindrome. How many minimum kms I need to travel so my car meter find another palindrome?
1
vote
1answer
274 views

The 100 Coins Puzzle

There are 10 sets of 10 coins. You know how much the coins should weigh. You know all the coins in one set of ten are exactly a hundredth of an ounce off, making the entire set of ten coins a tenth of ...
3
votes
1answer
151 views

Looking for a pattern in a math riddle

Looking to find a pattern but no idea how: $12\mathop{\square}21 = 86$, $13\mathop{\square}31 = 192$, $14\mathop{\square}58 = 389$, $14\mathop{\square}94 = \ ?$
-1
votes
2answers
115 views

I have a button…(story problem)

Tom has a job. He is a button pusher. He works for 8 hours per day. his job at work is simply to push a button. He has some freedoms and some limitations. When he arrives to work each day he has 5 ...
0
votes
1answer
284 views

Striking off a digit from each of the numbers written in seven rows, while preserving arithmetical operations

Problem Strike off any digit from each number in seven rows (need not be at same place) and combine the same operations with 3 digit numbers to get the same addition. After this strike off another ...
1
vote
3answers
316 views

Minimum number of objects required to figure out the issue

There 1,000 buckets, one of them contains poison, the rest of them are filled with water. They all look the same. If a pig drinks that poison, it will die within 30 minutes. What is the minimum number ...
0
votes
1answer
80 views

what is the minimum number of hints must be provide in a Sudoku with only one solution in order to reach the answer?

what is the minimum number of hints must be provide in a Sudoku with only one solution in order to reach the answer? Also if you are interested, please provide a reference.