# Tagged Questions

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A few nights ago I couldn't sleep and so started doing this: I would take a number and add up all of its digits to get a new number and then add up all of those digits and so on until there was only ...
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### Find A,B,C,D consecutive numbers based on written addition formula

$A, B, C, D$ are consecutive digits: $B$ is greater by $1$ than $A$, $C$ is greater by $1$ than $B$, $D$ is greater by one than $D$. Four $X$s are digits $A,B,C,D$ in unknown order. Find $A,B,C,D$ ...
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### Alphametics Question

In the figure below, each distinct letter represents a unique digit such that the arithmetic sum holds. If the letter L represents 9, what is the digit represented by the letter T? ...
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### Given a set of digits, what is the biggest number we can make using exponentiation - numberphile noodle quiz

The question is motivated by a question on a can of number noodles. Each item is a digit between $0$ and $9$. Clearly, if you form a string and consider it to represent a base $10$ integer, then ...
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### Clock Synchronization [closed]

There is a clock at the bottom of the hill and a clock at the top of the hill. The clock at the bottom of the hill works fine but the clock at the top doesn't. How will you synchronize the two clocks. ...
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### Number of songs sung.

There were 750 people when the first song was sung. After each song, 50 people are leaving the hall. How many songs are sung to make them zero? The answer is 16, I am unable to understand it. I am ...
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### How to solve multiplication alphametics?

I am referring to puzzles like these, where every letter represents a unique number (0-9): ...
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### How to solve this alphametic (verbal arithmetic)?

I know I can get the answer for this puzzle but I'm struggling to see how to solve it. Every letter represents a different number (0-9): ...
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### Puzzle: Representing age using digits from birth-year in order. Impossible cases?

I recently wrote my friend a birthday card and thought it would be fun to write her age using mathematical operations on the digits of her birth-year in order. For example she turned 36 and was born ...
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### Puzzle : There are two lengths of rope …

You have two lengths of rope. If you set fire to the end of either of them, the rope will burn in exactly one hour. They are not the same length or width as each other. They also are not of uniform ...
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### A rule to determine the crossed out digit

Lets take any integer, $z=abc\cdots$, form the sum of its digits, $a+b+c+\cdots$, subtract this from $z$, cross out any one digit from the result, and denote the sum of the remaining digits by $w$. ...
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### Is the solution to this holiday puzzle unique?

I read the following question on this site: Start at 2011. By moving through the maze and doing any arithmetic operations you encounter, exit the maze with a result of 2012. You may pass through an ...
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### Least characters in a numerical representation of integers

I was wondering what the shortest way to represent any given number is. For example, $387420489=9^9$. So, for this case, the smallest representation is of order 2 (2 numbers). Alternatively, ...
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### Is it possible to determine the profit percentage? If yes, then how?

A shopkeeper who professes to sell his goods at cost price, uses a faulty balance that has one arm 4% longer than the other. Is it possible to determine his profit percentage? If yes, then how? ...
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### Three numbers that multiply to ten (It gets harder)

I am working on a problem that involves the following: One must find three numbers, integers and/or decimals, that multiply to ten. Here's the catch: You must use all integers, $0-9$, in the ...
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### What's the maximum possible score in this mathy solitaire puzzle?

Consider a deck of 52 cards in four mathy suits --two red: "adds" ($+$) and "subs" ($-$); and two black: "muls" ($\times$) and "divs" ($\div$)-- and thirteen numerical values --"A" (1), 2, 3, 4, 5, 6, ...
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### Understanding Strategy:Minimum number of weighing to find the faulty bag

If Mr M buys $n$ bags of sands, each weighing a unit each except one bag. What is the minimum number of weighing is required to determine the faulty bag when: a two pan balance is used? ...
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### A puzzle from Perfectly Reasonable Deviations from the Beaten Track by Richard Feynman

The following is a puzzle I found while reading Perfectly Reasonable Deviations from the Beaten Track by Richard P Feynman. There are 2 shops which sell oranges.At Shop A you get 2 oranges for 5 ...