# Questions tagged [calculation-puzzle]

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

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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, ...
746 views

### Ernie and the Chance to Save a Beautiful Relationship

I should have smelt a rat when Ernie invited me to an event at the local club rooms, because when I asked why his wife was not attending, he replied that she had another engagement for that night. “I ...
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239 views

### Equilibrium of differences

There is a subtraction equation written on the board, with three digits minus three digits, and the first digits both fixed. Alice and Bob need to fill in the remaining 4 digits (A~D below) using 4 ...
• 654
124 views

### Multiple Line Lengths around 8 triangles

The image below contains 8 triangles each having side length 6. Inside each triangles are three numbers indicating lengths of 3 lines that are wrapped around the triangle without gaps. Numbers range ...
• 529
663 views

### 1000 digit sum calculation puzzle

I have 7 numbers that add up to the same value as the sum of the base 1000 digits of the product. Here are the numbers: 86, 203, 296, 395, 401, 407, 913 The first part of the puzzle is to understand ...
• 652
851 views

### Time (and a place) for an odd-one-out puzzle

This puzzle is part of the Monthly Topic Challenge #6: Is it really that [time] again?. It is a tough task to create an 'odd-one-out' type puzzle whose solution lacks any ambiguity at all - it is all ...
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### Trust me: you do not want to go down this road with me

Every cell has a digit from 0 to 9 or one of the four operation symbols +, −, ×, and /, signifying addition, subtraction, multiplication, and division respectively. No digit appears more than once in ...
• 11.3k
152 views

### Money in a piggy bank [closed]

In the attic of his house a man found an old piggy bank with twelve cents inside. He called two of his friends to come and see the antique piggy bank and asked them to put more money into the piggy ...
• 2,873
924 views

### Nifty Nines Impossibility Puzzle

Could someone please provide me the solution to this puzzle: 99 + 9 = 9? Professor Otto Doppelganger was one of Europe's leading puzzle experts. In the summer of 1899 he invented the Nifty Nines ...
• 71
239 views

### Tile and Error - When Seven Ate Nine

Ok folks, so the three overlapping ellipses form seven curved regions. Your job is to place all seven tiles so that each region has exactly one tile and each ellipse adheres to the corresponding ...
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3k views

### 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 ...
• 123
370 views

### Stuck on hard Kakuro

I‘m stuck on this Kakuro. Does anyone have any hints how to proceed? Thanks!
• 21
895 views

### Sergeant Sequence brings in the analysts

This puzzle is part of the Monthly Topic Challenge #5: On-and-onograms "We've intercepted another message, Chief." "Good work, Sequence. What does it say? Where is Terne now?" The ...
• 117k
222 views

### What is the biggest number you can make with 6 9s?

What is the biggest number you can make with 6 9s? These are the allowed operators: Subtraction Addition Multiplication Division Factorial Exponents Square root Floor and Ceiling functions Arbitrary ...
• 395
1 vote
178 views

### Trapped with a number puzzle

A family of your most hated Nggyupnglydown tribe has turned you into a vampire and trapped you in a chamber with a screen and some buttons on it, and you have to enter the code 4, 8, 15, 16, 23, 42 (...
• 509
1 vote
356 views

### Reviving the Ruins of Number Kingdom

The great wizard Factorial surveyed the empty buildings with an ever-increasing sense of dread. The staff of recursion he held was incredibly powerful and could do great damage in the wrong hands. In ...
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4k views

### Make e using 1, 2, 3, 4, 5, 6, 7, 8, 9

Can you make $e$ with the digits 1, 2, 3, 4, 5, 6, 7, 8, 9? You can only use the digits once. The allowed operators are listed beloẉ. Addition Subtraction Multiplication Division Square root ...
• 395
461 views

### Make the numbers 1-100 using 1,7,3,4

I made this puzzle myself. As the title says, you must make the numbers 1 to 100 using the numbers 1,7,3,4 - in that order. All numbers must be used. The allowed operators are below: Addition, ...
• 395
1k views

### What extra number did I form?

My friend and I are each trying to form the integers from $0$ to $100$ using the numbers $2, 3, 8, 9$. We are only allowed to use the five basic operations: addition, subtraction, multiplication, ...
• 3,660
401 views

### How many digits does $7^{100}$ have?

I'd like to estimate $7^{100}$ without using these new-fangled computers everyone is talking about, but I think I need your help. Please estimate $7^{100}$ without the use of a computer. My friend ...
8k views

### The computer can't do anything I couldn't do with pen and paper

If you want to know how much $3^{100}$ is, you can just type it into a computer and it will spit out a really big number. But that is no fun. The task is to estimate $3^{100}$ with some computation ...
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150 views

### Can you Avoid the Spear-Wielding Gladiator?

You are trapped in a circular coliseum, and a gladiator with a spear is chasing you. You can't defend yourself, but you can run faster than the gladiator. You run at 11 feet per second, and the ...
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750 views

### A Pubular Puzzle

Try to make sense of the puzzle below. Circle1, circle2, circle3, circle4, circle5, circle6 and circle7 have radius r1, r2, r3, r4, r5, r6 and r7 respectively and periferi p1, p2, p3, p4, p5, p6 and ...
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### a six-by-six KenKen

The rules of KenKen are as follows: You must fill in the numbers 1 through 6, one number per box, in the grid, so each row and each column contains each number exactly once. Each heavily outlined ...
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367 views

### Dark time in prison

You wake up. It is pitch dark. You don't know where you are. You feel groggy. The last thing you remember is being in a bar, a sexy young woman appeared out of nowhere, walked straight at you, ...
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102 views

### Three planes fuel tanks for less than halfway around the world - how can one plane make it around the world and what is the minimum fuel tank size?

Inspired by this recent question here is a variation. Three identical aeroplanes are based on an island with one airport. Each plane can take fuel to get less than halfway around the world. Fuel can ...
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285 views

### Magic: The Gathering – projecting images

You are in a Magic: The Gathering commander game. It is now your first main phase and you control these permanents: One Miirym, Sentinel Wyrm: "Whenever another nontoken Dragon enters the ...
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### Why are all numbers from 1 to 2N covered by weights with powers of 3?

This is from 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 N pounds ...
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138 views

### Find the 3 Item Amounts

Last week the store's receipt printer removed lines randomly from each item amount. A technician repaired the printer, but now it adds lines randomly to each item amount! The cashier told me that for ...
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584 views

### A number association puzzle

These 0 to 10 digits are associated with the specific numbers as shown below. What are the associated numbers for digits 9 and 10? Why? Bonus: Is there an associated number for 11?
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743 views

### Find the Two Item Amounts

I bought 2 items yesterday and the receipt was incorrect, so I asked the cashier about it. She told me that The receipt printer had been acting funny recently. The total is always correct, but some ...
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709 views

### What is 12 in this same pattern?

7 = 31674ZS 8 = 883011SO 9 = 166037352UR 10 = 434782608W...
728 views

### Compact mathematical expression [closed]

Make a mathematical expression whose value is equal to 2 that uses all the digits 0, 1, 2, ... 9 exactly once and uses as few other mathematical symbols as possible.
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### Some doctors and a lot of hand shakes

At a congress there are some doctors, and everyone shakes a certain number of hands (never more than once with the same person). The doctors can be divided in two groups: -Group O: the doctors who ...
• 355
101 views

### How many colleagues went to Starbucks?

You go to Starbucks with some colleagues, everybody gets a cappuccino. Every cappuccino contains only coffee and milk (at least some coffee and some milk) and no other ingredients, but everyone has a ...
• 355
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### Patrick and Rachel go to a tennis tournament with 7 other couples

Patrick and Rachel go to a tennis tournament with 7 other couples. Each round is a single's match (1 vs 1). Nobody plays against his/her partner and nobody plays twice against the same player. At the ...
• 355
153 views

### Productive Neighbours

Seven tiles need to be placed so that one is placed in each of the curved "regions" formed by the three circles. One tile has been placed for you. Each circle has a corresponding statement. ...
• 2,250
346 views

### Problem XXX (Squared) - Number Stile

Happy weekend folks, The intersections of the three circles divide their interiors into seven "regions" By complete non-coincidence, we have seven tiles A "valid" placement is one ...
• 2,250
123 views

### How to fill up the numbers in a set of empty discs drawing a pentagon? The target sum is 10 [duplicate]

Can anyone explain to me the math behind the problem? I want to convert the mathematical solution into an efficient algorithm. The target sum can be any given number. For reference please check the ...
204 views

### Summa Cum Laude - Tile and Error

For any set X, {X} denotes the sum of its elements. "I divide {A}" means all items in that set are divisors of the sum of A's elements. Arrange the tiles so that four are in each set and the ...
• 2,250
1 vote
188 views

### Solve for 69 using only 1 9 9 2 in that order [closed]

You must use all the digits of $1 9 9 2$ in that order to come up with $69$ as the answer. For example $- (1 + \sqrt {9})! + 92 = 68$ but you must solve for $69$.
167 views

### Twenty (or fewer) questions to solve a three-digit code

In an episode of Odd Squad, the squad are left with five yes/no questions to get a three digit code out of a villain. Luckily for them, they have sufficient questions to guess the first number by ...
• 5,182
394 views

### Determine the highest possible sum of all faces of cube

There is a non-negative integer written on all six faces of a cube. Integers on all possible three common adjacent faces (all faces are adjacent to each other) are multiplied and then they are added. ...
• 1,270
756 views

### Only one such number exists

A 5 digit number ABCDE is divided by 2,3,4,5,6 and gives A,B,C,D,E as the remainders respectively. Can you find the only possible number? This was asked in my math exam, I think it would make a good ...
• 1,270
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### Strategic betting on the world series

Your wealthy father-in-law gives you \$10000 to place a "double-or-nothing" bet on Boston Red Sox in the World Series [1]. In other words, your father-in-law expects to receive \$20000 if ...
• 486
200 views

### A number of ten different digits, divisible by 8, 9, 10, and 11

Each of the digits 0 through 9 is used exactly once to create a ten-digit integer. Find the greatest ten-digit number which uses each digit once and is divisible by 8, 9, 10, and 11.
159 views

### The peculiar inequality [closed]

Let's have the following relation $\sqrt[3]{\frac{(x+1)^3+x^3}{2}}\lessgtr\frac{2x^2+2x+1}{2x+1}$ where $x$ a positive integer greater than zero. Which inequality is valid?
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1 vote
151 views

### Zettler's Encyclopedia

On epiphany 1735, Sir Zettler, who was a great publisher from the old continent, promised to issue a "Great Universal Encyclopedia of Collectible Wisdom". It was meant to be affordable for ...
3k views

### Turn the dials until each of the 12 columns add up to 42

I received the wooden puzzle below for Christmas. After playing with it for a while I decided I needed to actually write something down if I was going to solve it. Eventually I just wrote an algorithm ...
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What is the trick you need to use to be able to express the quantity $(4x^4+8x^3+7x^2+3x+\frac{1}{2})$ as the difference of two squares? addendum: The answer contains only rational numbers greater ...