Tagged Questions

This tag is meant for questions about the mathematical principles behind games, riddles, or their possible solutions. If the answer is known to you please do not use this tag to "riddle" other users, but rather to ask about the correctness of a possible solution or ways to extend and improve an ...

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Crossing the River Story Problem

A group of adults and children go on a camping trip. On the first day, they come to a river too deep to wade across. They find a small canoe which can carry either one adult or up to two children at ...
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how to determine the day of the week when some clues are given?

In a year, there are more Mondays than Fridays, and more Sundays than Wednesdays. Which day of the week is the first day in March of that year?
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Mental calculation of the day of birth [closed]

I have a friend who can tell the birth day of anyone by only knowing the date and year. He is able to do this almost instantaneously. How does he do it? Please enlighten me on this subject. Thanks a ...
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A man can cut the grass in $T$ minutes What part of the lawn can be cut in $30$ minutes?

A man can cut the grass in $T$ minutes What part of the lawn can be cut can be cut in $30$ minutes? Options: a) $\frac{30}{T}~~~~$ b) $T-30~~~~$ c) $\frac{T}{30}~~~~$ d) $30-T$ My approach: ...
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Coin toss puzzle with 1 biased and 2 unbiased coins

Three coins are given: one two-head coin and two fair coins. You randomly choose a coin and the first three tosses give heads. What is the probability that 4-th toss is a head. I have two solutions ...
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Word problem involving equality of multiplication and addition

The problem is: Johnny is at his local news-stand, looking at the various magazines on display. He picked up three magazines, $A$, $B$ and $C$. He passes the magazines to the shopkeeper, who ...
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One Million Proficiency Efficiency Calculations

I have been playing the "Million" game on my apple device after discovering it through the trending applications in the search function. After beating the game I began to wonder to myself if there was ...
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Maximize the earning of thieve [duplicate]

Two cheeky thieves counted a total of exactly 1 billion $\left(10^9\right)$ dollars in the bank vault. Now they must decide how to divide the booty. But there is one problem: the thieves have only $M$ ...
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Today in math class, a number puzzle arose where you would have to find a 10 digit number, where each digit describes the number of other digits in the number, for example: $$\text{0 1 2 3 4 5 6 7 8 ... 2answers 80 views Mathematical logic problem [closed] Six robots are pointing fingers at one another. A: C is faulty. B: Either A is faulty or C is good. C: Either D is good or E is faulty. D: F is good. E: Either C is good or ... 0answers 124 views How many open knight's tours are possible in a 3×16 chessboard? [closed] According to the following page (http://magictour.free.fr/enum), 17269264 open knight's tours are possible in a 3×16 chessboard. I compute the number by using the following code(C) and the number is ... 1answer 58 views A man returns home from a two month trip and discovers that his enemies have put a moat around his property. A man returns home from a two month trip and discovers that his enemies have put a moat around his property. The property consists of a 108×108 foot square centered within a 140×140 foot square, and ... 1answer 43 views Totally puzzled by calculating distance I'd be behind Usain Bolt if I competed with him I'm a simple man living his life and enjoying every moment I get. I don't know much mathematics and I need a little bit of help figuring out the following puzzle. Today I found out about world ... 0answers 46 views Puzzle about decomposing numbers with +, -,\times, \div In the book The Moscow Puzzles by Kordemsky I came across the following puzzle (no. 47): Express 100 three ways with five 5s. You can use brackets, parentheses, and these signs: +, -,\times, ... 2answers 78 views Riddle : Given an integer power, does any integer to this power start with the power? I initially found the following riddle somewhere : Is there an integer n such that n^{2004} starts (from the left) by 2004 ? I was unable to find an answer, but I found the question rather ... 2answers 67 views Checkpoints along a Highway This is a new puzzle I'm creating. Advices welcome. Preliminaries: Imagine a car highway. This highway can be described as the smooth connection of smaller segments consisting of straight lines, and ... 5answers 54 views A puzzle regarding marks! In a exam there are 50 questions. +1 for correct, -1/3 for incorrect and -1/6 for unattempting. Sarah scored 32 in that exam. Find the minimum number of questions she must have done wrong. How can I ... 3answers 239 views What is solution to this maths series problem? [closed] I found this question on facebook and me and my friend were discussing the possible solution for 9. We have found 3 answers and none of us has any idea which one is correct as all of them looks ... 2answers 70 views Can any n \in \mathbb{N} be reached from 1 by doubling and summing digits? For n \in \mathbb{N}, let f(n) = 2n and let g(n) equal the digit sum (in base ten) of n. Can any n \in \mathbb{N} be reached from 1 after a finite series of applications of f and g? 2answers 63 views Looking for set of combinatorics problems I'm preparing to Mathematics for Computer Science exam. What I learned from past edition of exams is fact of very often occurence of old problems. I mean more or less known problems, but possible to ... 1answer 34 views How many of the three natives are bears and how many are packers? [closed] In a certain mythical community, Bears always lie and Packers always tell the truth. A stranger meets three natives And asks the first if he is a bear. The first native answers the question. The ... 3answers 246 views Fun logic puzzles to teach logic/proof-writing to students Forgive me if this is too soft of a question, but I am looking for some fun, quick, and interesting logic puzzles to give to my students. I'm teaching an honors calculus course, and this will be their ... 0answers 44 views Guess the rule of transformation of a natural number I came across a playful problem. On a sheet of paper it is written the number \overline{1234xy}, where $$\overline{1234xy}=1*10^5+2*10^4+3*10^3+4*10^2+x*10^1+y$$ Five ... 1answer 92 views parallel resistors Consider the set E_b = \left\{1, 1.2, 1.5, 1.8, 2.2, 2.7, 3.3, 3.9, 4.7, 5.6, 6.8, 8.2\right\}. This is our base set. Let's define the set E as follows:$$ E = \left\{ 10^k e \mid k=0,1,2,\ldots, ...
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Three players, Annie, Billy and Katie, each have a natural number written on their foreheads. Each player can only see the foreheads of the other two. The following two things are common knowledge ...
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A Solution to the Classic “12 Marbles, find the one of different weight” Brainteaser

The classic problem goes like this: You are given a set of scales and 12 marbles. The scales are of the old balance variety. That is, a small dish hangs from each end of a rod that is balanced in ...
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All squares above 6 have an even number of multiples of 10. Why?

I was recently looking at a puzzle in Martin Gardner's book: Two brothers sell their heard of sheep, and receive the same number of dollars per sheep, as there were sheep in the heard. They ...
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Fixed points of iterates of a certain map $\Bbb N \to \Bbb N$

I have stumbled onto chains of numbers that are interesting in that, when they are split up into their digits, summed, squared, and repeating some number of times, yield the original number. This ...
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The locker puzzle - predetermined strategy

The question is related to the famous locker puzzle: The director of a prison offers 100 prisoners on death row, which are numbered from 1 to 100, a last chance. In a room there is a cupboard with ...
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Dartboard puzzle.

Given a dartboard of radius r and infinite darts.How many minimum darts you need to throw so that you can be sure that the next dart you throw is strictly less than r distance from some previous dart? ...
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A probability puzzle about mountain villages

I hope this puzzle will be of some interest. The mountain villages $A,B,C$ and $D$ lie at the vertices of a tetrahedron, and each pair of villages is joined by a road. After a snowfall the ...
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Proving that an expression returns a real non-integer number (Number 2)

Let $$a=443372888629441 = 17*31*41*43*89*97*167*331$$ $$b=(3+\sqrt{13})/2$$ $$c=(2+\sqrt{8})/2$$ $$d=(1+\sqrt{5})/2$$ How can you prove that the expression ...
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A puzzle about numbers which do not have 2 in their decimal representation

I came across this puzzle recently which I hope people might enjoy. Let $S(n)$ be the set of positive integers less than $n$ which do not have a $2$ in their decimal representation and let ...
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Strategy for identifying traitors

I started playing the game Lost Dimension recently, and will reproduce the logic problem of the game here. Note that this would therefore have some implied spoilers from that game, although not beyond ...
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What is this problem called - 4 blocks and 3 rods?

I can't seem to recall the name of this problem however, I do remember part of its description. Basically, there are three 3 rods similar to those of an abacus and on one of the rods there are 4 ...
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Relation to find the last standing person in a circle. Possible variant of Josephus problem

Consider a set of N people standing in a circle, we kill the first person, spare the second, kill the third person and so on.. Find the last standing person in the circle. I think this might be the ...
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solve the puzzle

I have recently encountered a reasoning question that I have solved half , but I can't solve one part of it. Question : \begin{align*} 3 + 5 + 6 &= 152092\\ 7 + 6 + 5 &= 422416\\ 4 + 7 + 5 ...
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Proving that an expression returns a real non-integer number [closed]

Let $$a = 443372888629441$$ $$b = \frac{2+\sqrt{8}}{2}$$ $$c = \frac{1+\sqrt{5}}{2}$$ How to prove that the expression $$\frac{b^a-b^{-a} - 2(c^a-c^{-a})}{a}$$ is a real non-integer number?
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Relation/ formula to Find the last person standing after removing people alternatively from a line?

Given N number of people, each marked as a number starting from $1$ through N, standing in a straight line where you remove folks alternatively from a line. For example in iteration 1: You would ...
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mathematical puzzle [closed]

If you have free time you can try to solve next mathematical puzzle. Given are four integers: 1, 3, 4, 6 and also four basic operations: multiplication ...
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Can you complete the expression $2 \underline{ }\, \underline{ }\, \underline{ } \,\underline{ } 5 = 2015$?

Can you complete the expression $2 \underline{ } \, \underline{ }\, \underline{ } \, \underline{ } 5 = 2015$ and make it correct by replacing two underscores with a selection of the ...
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Is there a pattern present?

Jack is looking at Anne, however Anne is looking at George. Jack is married, George isn't, and Anne's status is unknown. provided this info alone determine whether: a) A married person looks at a non ...
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puzzle 3-d visualization

729 small cube are painted pink on each face and then arranged to form 27 identical middle-size cubes.Each middle size cube is painted black and then arranged together to form one large cube. And ...
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I've encountered this question and found two "contradictory" answers to it. of course they are not really contradictory, but I'm having some trouble explaining why not. Say there is a frog standing ...
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find a group of lowest N numbers so that no 2 pairs have the same bitwise or

I am trying to find the lowest group of N numbers (i.e. N=1000) so that no 2 pairs from the group have the same bit-wise or. more specific need to find a group $A = \{a_1,a_2,a_3,..,a_N\}$ such ...