# Questions tagged [calculation-puzzle]

A puzzle that involves numerical calculations, such as multiplication and addition.

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33k views

### 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?
13k views

### Making π from 1 2 3 4 5 6 7 8 9

There have been two other questions here and here that are similar to this one, but this changes the rules up a little. Your job is to approximate $\pi$ using the sequence of digits (in order): 1 2 ...
52k views

### 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

### Can you explain these equations?

Anthony just got a new drone with an HD camera and microphone, and he is eager to test it out. He connects his computer to its wireless live video stream, opens up his window, and flies it outside. ...
6k views

### 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?
15k views

Suppose you have 100 lbs of cucumbers and these cucumbers consist of 99% water. You decide to leave the cucumbers in the sun for a while until they consist of 98% water. You bring the cucumbers back ...
150k views

### 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 ...
12k 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 the ...
5k views

### My grandfather's socks

My grandfather has a big drawer where he keeps his socks. The drawer contains more than 900 but less than 1000 individual socks. Each of his socks is black or blue, and there are more blue socks than ...
4k views

### Ernie's automatic parking valet

I was helping Ernie out in his shed a while back, when his favorite screwdriver suddenly wore out. I offered to go and pick up a new one for him and Ernie thought it was a great opportunity to test-...
12k views

### 3:3! It's a football score! [closed]

Given to me, by a friend: How would you make 20, using two threes? You may use any basic operation. And others, such as square roots (the symbol), factorials, etc. Any operation is allowed. Just ...
7k views

### Rendering the number 10,958 with the string 1 2 3 4 5 6 7 8 9

Brazilian mathematician Inder Taneja has found a way of expressing every number between 1 and 11,111, except 10,958, by inserting mathematical operators in between the numbers 1 2 3 4 5 6 7 8 9 and ...
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### Mr. Hilbert and the Problem of the Erroneous Equation

Having had just checked into the Grand Hotel, Mr. Hilbert slumped into the hotel room armchair with relief. Finally he could have some peace and quiet and solve the quaint riddle his colleague gave ...
2k views

### The Nuclear Missile Standoff

Three world powers have just entered a nuclear war! They have been waiting for this day for decades; everyone has their nuclear missiles ready to fire, and only need to choose a target. The Chinese ...
780 views

### Integers around a circle with consecutive pairs adding to a square

The integers 1 to 50 are placed around a circle in such a way that the sum of any two of them which are adjacent is a perfect square. Of these integers, the even numbers are then removed. Restore them....
9k views

### 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 ...
8k views

### 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 ...
2k views

### Computation without a computer

In the number $(1+\sqrt{3})^{2015}$, what is the 224th digit after the decimal point? You may NOT use a calculator, computer, or any electronic aid to answer this question. Only pen(cil), paper, and ...
3k views

### Ernie and the Alchemist's Gift

For Ernie, the task of choosing Christmas presents for his friends is always a struggle. I think that is because, while he finds it easy to solve problems relating to machines, mathematics, and ...
9k views

### Using only 1s, make 29 with the minimum number of digits

Use the minimum number of ones to make 29. Here is the list of operations permitted: "Standard" operations, such as: $x+y$, $x-y$, $x\times y$, $x\div y$ Negation: $-x$ Exponentiation of two numbers:...
9k views

### How many steps are visible on the Escalator?

Alice walks down an upward escalator and counts 150 steps. Bob walks up the same escalator and counts 75 steps. Alice takes three times as many steps in a given time as Bob. How many steps are ...
5k views

### How many consecutive positive integers can you make using exactly four instances of the digit '4'?

Starting at 1 (which is 4 - $\sqrt4$ - 4/4), how many consecutive integers can you make using exactly four instances of the digit '4'? Basic rules: Any operator symbol is "free". Any printed '4' ...
2k views

### Making Things Difficult

An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Factoring the Time Think fast! If you're looking for meaning, these clocks have some for you. Keyboards are Disgusting Gunky ...
36k views

### Create all numbers from 0-100 only using all of 1,2,3,4 and 5

Create all numbers from 0-100 only using 1,2,3,4 and 5. No repeats and you have to use each number. Also, you can use any operation. I've only gotten to 50 by pure brute force. I think that this might ...
6k views

### Make 11 from five identical digits

At a tender age my father introduced me to an arithmetic game: making the number 11 from five single digits using only the basic operators listed here: ...
3k views

### Five loaves and the extra traveller

Two people are travelling together. One of them has three loaves of bread; the other one has two. At some point they stop to eat lunch. A third traveler that happens to walk by joins them. They split ...
5k views

### How do I convince my grandmother?

How do I convince my grandmother (who really hates mathematics) that there exist three positive integers $x,y,z$ that satisfy the equation $28x+30y+31z=3650$?
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### A game of multiplication and addition

Carol is playing a game with Alice and Bob. She secretly chooses two integers between 1 and 10 and gives the sum to Alice and the product to Bob. After some time, the following discussion occurs: ...
2k views

### How many silver marbles does Paul have?

Peter, Paul and Mary have between them 282 marbles. Though of the three friends, it is Peter who has the most marbles, he is the one with the fewest silver marbles, just the square root of the ...
3k views

### What, the answer isn't the No of the Yes is?

Doorknob knows exactly how to solve this, so I ask him to not answer this question. Well, here's the puzzle: No, an answer is the cube without A, No? The Yes is No. The squared answer, Yes, is to an ...
11k views

### The largest integer made of 1,2,3,4

What is the largest integer $A$ that can be produced from the four digits $1,2,3,4$ subject to the following rules? Each of the digits $1,2,3,4$ is used exactly once. Juxtaposition of digits is ...
4k views

### How many flowers to buy? [duplicate]

A man decided to place some flowers on three different temples. There is a magical pond before each temple and he has to swim through each one. So his trip will be: [ pond1 - temple1 - pond2 -...
1k views

### My calculator seems to be broken

Damn... Here I am, in front of my examination paper, and my calculator is failing me! I can do some calculation, but for some additions, I don't get the good result! (I think my roommate purposefully ...
6k views

### 3x3 “Magic Square” of Prime Numbers

During the thinking and analysis of some mathematical problems, I came up with this puzzle: Just like any magic square, one has to fill in $9$ different numbers $P_1, P_2, \dots P_9$ to a $3 \times 3$...
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### 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 of ...
1k views

### A diabolical puzzle: Hector + Tisiphone =?

Homer + Ovid = Paris Ulysses + Julius Caesar = Nimrod Guy de Montfort - Cleopatra = Medusa Epicurus - Pluto = Dido Hector + Tisiphone = ?
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### SPEND LESS MONEY alphametic

The well-known verbal arithmetic problem S E N D + M O R E ----------- M O N E Y explains (or at least it did the first time I knew about it) the story ...
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### The Prison Escape Pt. 1 (THE DOOR)

You are currently escaping a prison owned by a mad scientist. As you were about to approach a large iron door that you think should be leading to the exit, a guard came out from the shadows. ...
774 views

### Honeydripping around the clock

What path could a honeybee follow, beginning and ending at top center, visiting every empty cell exactly once and dripping 2 drops of honey into the last cell? Start ...
9k views

### Number 88 from the digits 2, 0, 1 and 7?

Can you use the digits 2, 0, 1 and 7 each only once to create the number 88?
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### How to get 5 from 0,0,0 and 1?

Can you use the digits 0,0,0 and 1 each only once in a mathematical expression for the number 5 using only common mathematical symbols with at least 1 mathematical symbol between each number?
5k views

### A New Math Operation?

Your quirky Math teacher comes with a new Math operation called "@" and wants to see if you can figure out what it does. She writes the following examples on the blackboard: 8@5 = 31340 9@3 =...
5k views

### You're invited! Now what?

(semi-interactive puzzle) BRIIING! BRIIING! BRIIING! You wake up with a start. It's 6:30... already!? Darn. You roll slowly out of bed, preparing for the day ...
5k views

### Add parentheses to make this true

Add parentheses to the following to make a true equation: $10-9\times8-7\times6-5\times4-3\times2-2\times1=1$
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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 ...
3k views

### Dwarfs over bridge problem

300 dwarfs go over a bridge in the middle of the night. The bridge is rickety and manages at most two dwarfs at a time. With them is a lantern that they must provide at each transition. Dwarfs need ...
2k views

### Ernie and the Alien Invasion

Yesterday I dropped in on Ernie to show off my new j-watch. Ernie wouldn't be impressed by instant wrist-mounted access to social media sites like me-tube, tweeter and farce-book so I thought I would ...
1k views

### Which is larger? $\sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2}$ versus $5$

Which side is larger? $$\sqrt{15} - \sqrt{7} + \sqrt{5} + \sqrt{2} \stackrel{?}{\lessgtr} 5$$ Without using a calculator, computer, or estimating square roots, please determine which side has the ...