# Questions tagged [calculation-puzzle]

A puzzle that involves numerical calculations, such as multiplication and addition. Use with the [mathematics] tag.

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### A camel transporting bananas

A somewhat well-known puzzle is described as such: You have a pile of 3,000 bananas. You wish to transport them to a place 1,000 miles away on the back of a camel; however, the camel can only carry ...
3k views

### How do I tell the children's ages?

My friend once told me a logic puzzle along the lines of: A student asks a teacher what the ages of the teacher's three kids are. The teacher said, "the product of their ages is 72, and the sum ...
16k views

### I don't know the two numbers... but now I do

Two perfect logicians, Summer and Proctor, are told that integers 𝑥 and 𝑦 have been chosen such that 1 < 𝑥 < 𝑦 and 𝑥 + 𝑦 < 100. Summer is given the value 𝑥 + 𝑦 and Proctor is given ...
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### A Set of Water Jug Challenges

You've probably heard about challenges with water jugs, so why not try a few? Use 3- and 5- liter jugs to get 4 liters. Use 5- and 7- liter jugs to get 4 liters. This one's different. How many ...
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### Use 2 0 1 and 8 to make 67

Use $2$ $0$ $1$ and $8$ to make the number $67$ RULES You must use all 4 digits. Only the digits 2, 0, 1, and 8 can be used. You can make multi-digit numbers out of the numbers. Examples: 20, 82, ...
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### Write twenty-four from four numbers

Write 24 using the four numbers 1, 3, 4, 6 and basic arithmetic. Explanations: The given are numbers, not digits, so you can't group them using decimal notation. For example, you can't create the ...
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### What's the fewest weights you need to balance any weight from 1 to 40 pounds?

Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a two-sided scale by placing a certain combination of these weights onto ...
446 views

### Shortest number of attempts to solve this issue [duplicate]

There are 9 identical balls but only one of them has a higher weight. You are also given a weight balance. How many attempts would you require to identify the ball with the extra weight and how?
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### How can 64 = 65?

Here is a interesting picture with two arrangements of four shapes. How can they make a different area with the same shapes?
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### 1 2 3 4 5 6 7 8 9 = 100

The sequence of numbers $1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9$ has the property that you can insert mathematical operators in between the numbers from $1$ to $9$ and make the expression evaluate to 100. For ...
7k views

### N pirates steal their share of bananas to the benefit of a monkey

The following is a type of logic / math puzzle I've yet to see on this site. I feel it belongs because the kernel of this problem can be reworked into other puzzles. $N$ pirates find themselves ...
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### Product and Sum

My fellow mathematicians Paul and Sam are very fond of mathematical puzzles. One day, I came up with the idea on mathematical puzzles while three of us having lunch together. I: Hey, guys. I am ...
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### Who gets more money?

There are two people eating bread. One of them has 5 loaves of bread; the other one has 3. They invited a third person to eat with them. They ate all 8 loaves of bread, and out of appreciation he gave ...
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### Travellers across a desert

This is a problem I once found in a math textbook a tutor used with me. A group of explorers is trying to get from their base camp to another camp which is eight days' walk through the desert. ...
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### A modified version of apples and oranges logic

Question: You have 3 baskets, one with apples, one with oranges and one with both apples and oranges mixed. Each basket is closed and is labeled with ‘Apples’, ‘Oranges’ and ‘Apples and Oranges’. ...
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### One beer too many

You're standing outside your apartment building after a late night out, with perhaps one beer too many, and you realize you have completely forgotten the code to get in. Luckily, you're a mathematical ...
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### Where has Jones lost 1 Rs?

Jack and Jones are brothers and they both sell apples for living. Jack sells 2 apples for 1 Rs and Jones sells 3 apples for 1 Rs. They each have 30 apples. Hence, Jack earns 15 Rs a day while Jones ...
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### 2x2 row and column equations

Rules: No paper or notes, but a calculator is accepted. Post the exact time min wise of how long it took. And obviously give the answer.
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### The last number on the blackboard

The numbers 1, 2, ..., 500 are written on a blackboard. Each minute any two numbers are wiped out and their positive difference is written instead. At the end only one number remains. Which values can ...
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601 views

### Two honeycomb hints (yet another 'find the next number in the sequence')

Find the next number in the sequence $1,7,74,\dots$ First hint: Second hint: To clarify: the 'hints' are really clues. They are hidden, because any of the two alone could be enough to solve the ...
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### Puzzle of putting numbers 1-9 in 3x3 Grid to add up to 15

In a 3x3 grid, I'd have to put numbers from 1 to 9 in a manner so that respective row, column and diagonal add up to 15. I have only been able to come up with one solution: 6 1 8 7 5 3 2 9 4 ...
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### A self-referring number

Find a ten-digit number with the number of zeros in it as the most significant (leftmost) digit, the number of ones as the second most significant digit etc.
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### Another Way to Count Sheep At Night in Bed

I came across this puzzle: A wayfarer asks a shepherd how many sheep he has. He replies that if he numbered them two and two, or three and three, or four and four, or five and five, or six and six, ...
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### Aside from brute force, how can I solve this puzzle?

Once upon a time, and old lady went to sell her vast quantity of eggs at the local market. When asked how many she had, she replied: Son, I can't count past 100 but I know that: If you ...
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### Correct way to add 22 to 4 to get given value

I was asked this logic puzzle in an interview. Tell me a correct way by which adding 22 to 4 will give 2. I asked interviewer what is the base of those numbers. He told that those are decimal ...
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### What is a Surpassing Phrase™?

If a phrase conforms to a certain rule, I call it a Surpassing Phrase™. Use the examples below to find the rule. Some details to save you time: 1. Font doesn't matter. 2. The number of words ...
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### The Mexican Standoff

There are three cowboys in a Mexican standoff against each other, named Juan, José, and Jorge. Juan is the straightest shooter in the West, and can hit his target 100% of the time. José, who has a ...
2k views

Background Story A nomad is injured in the desert. And he can't move, but fortunately an oasis is nearby, and he can stay there for enough time until rescue arrives. But the water is a magical water, ...
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### Simple Math Problem #1

Here is a simple math problem. Can you solve it? Examples: 678+57-24*2 = 7 265+34-12*3 = 8 328+58-22*1 = 12 Problem: 541+13-21*0 = ? HINT 1: Will see if this hint makes any sense or will edit ...
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### Four dice puzzle: 2,2,4,5

Damiano has thrown four dice and the numbers 2, 2, 4, 5 showed up on top. Damiano asks himself: What is the smallest positive integer that cannot be generated with these four numbers according to ...
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### "Magic: the Gathering" Challenge #5: What if Pod was One of Us

Previous Challenge Next Challenge BACKGROUND: The usual magic rules apply here. Please be explicit in mana usage in your solution where relevant. I've tried to ensure that there are no infinite ...
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### Odds of duplicate birthdays

I found the following problem in an number of places online: John once bet a fellow gambler that two of the first thirty persons they met and spoke to would prove to have the same birthday. Strong in ...
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### An Hourglass Puzzle

This puzzle follows from the well known sand timer puzzles: A Sand Timer Challenge http://www.crazyforcode.com/sand-timer-puzzle/ http://www.cut-the-knot.org/hg_solution.shtml Warmup: You are given a ...
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### A Sand Timer Challenge

Which (if any) of these intervals is it possible to measure given two sand timers (which change from question to question)? There are no minute marks, halfway points, etc. A. 7 minutes with 4- and 5-...
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1 vote
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### Magic: the Gathering - Challenge #6.b: It's Gonna Cost You

Previous Challenge Next Challenge Background Alright I'm going to try a more clear approach to my last attempted puzzle. Given the mana costs given below, name cards with those exact mana costs ...
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### Where is Jennifer's husband?

Jennifer is 21 years older than her son Douglas. 6 years from now, Jennifer will be 5 times as old as Douglas. Question: Where is Jennifer's husband most likely to be right now?
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### Display a number using a scientific calculator with most keys are stuck

Your have a scientific calculator such that most of the keys are unable to be pressed. The only keys that work are those for the functions  x^2 \;\; \sqrt{x} \;\; x!\;\; \exp\;\; \ln\;...
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### What does this mathematical operator do?

The solution to this puzzle is one I came up with when working on this puzzle: What is the answer of this math puzzle? For two natural numbers a,b, can you figure ...
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### This new puzzle type needs a name {5}

I believe I have invented a new type of puzzle... What is its name? Colour-blind-friendly version available here. Begin by solving the 9x9 sudoku; each of the 9 symbols ...
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### A truly amazing way of making the number 2016

Find a mathematical expression that yields the value $2016$ while obeying the following rules: Each of the digits $1,2,3,4,5,6,7,8,9$ is used exactly once Decimal points are allowed You may use ...
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### How many distinct unsolvable Rubik's cubes exist?

I wanted to answer this question: Why can't I have only one edge piece flipped on a 3X3 Rubik's cube? by saying that it is homomorphic to the illegal state in this question: Why is a ...
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### "Magic: the Gathering" Challenge #2: Two Peas in a Pod

Previous Challenge Next Challenge BACKGROUND: Here's a puzzle for Magic: the Gathering players out there. I feel that this puzzle is in the scope of the site, and is no different than other puzzles, ...
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### Rybo switched the calculator keys!

I'm Dave. In revenge for my calculator key-switching prank, Rybo has performed a similar prank on me! My calculator has the usual number keys, and keys for the usual four arithmetic operations: ...
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### For how long did Lisa walk?

Lisa gets picked up from work by her husband at exactly 4 pm every day. One day Lisa finished work half an hour earlier and started walking to meet up with her husband. She met her husband on the way, ...
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### 1 2 3 4 5 6 7 8 9 = 1

This question inspired me to write the same puzzle but instead replace the "= 100" with "= 1" with similar requirements and restrictions. What is the expression with the fewest number of operators ...
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### Four ones and four zeros

Which is the smallest natural number that can not be expressed in base 2 with precisely four ones and four zeros using the four basic arithmetic operations, exponentiation, concatenation, brackets, ...
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### Labelling a Snow Flake Graph to Attain Minimum Sum

Label the vertices (or nodes) of this graph with positive integers so that any two nodes are joined by a edge (or line) if and only if the corresponding integers have a common divisor greater than 1 (...
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### Create 76 out of 1,2,3,4

You can use +,-,*,/,^,! and sqrt operations (no concatenation) and all numbers must be used once and only once. for example, 75 can be made by $3×(4!+2-1)$ and $81=(2-1)×3^4$ I've been trying to reach ...
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### Find the 4-digit code!

An agent has created a 4 digit code from the result of a maths equation involving all the digits 1-9. We know where the number 3 appears in the multiplication, but not any of the other 8 digits. <...
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This is a follow-up to "A truly amazing way of making the number 2016": For every positive integer $n$, find a mathematical expression that yields the value $n$ while obeying the following rules:...