# Questions tagged [arithmetic]

For puzzles involving addition, subtraction, multiplication, or division.

109 questions
Filter by
Sorted by
Tagged with
4answers
6k views

### The mother of all age-of-the-captain riddles

A few days ago, as I was delving into the mess in my grand parents' attic, I found an impressive ancient book that was written in a language that I had never seen before. "This book is a collection ...
12answers
15k views

### XOR - Is it possible to get a, b, c from a⊕b, b⊕c, a⊕c?

Just got a simple question from a friend; still thinking. Let's share it! Is it possible to get a, b, c when you have a⊕b, b⊕c, a⊕c ? where ⊕ is the boolean ...
1answer
1k views

### Self-referential Sudoku

I built this a while back but never had a good forum for it; this seems like the perfect spot to turn it loose. This is a 'traditional' Sudoku; cells are filled with numbers from 1 through 9, and all ...
4answers
5k views

### Find average age without revealing your age

Ana, Barbara, Carol and Diana want to know their average age. But no lady wants to disclose her age. They decide a strategy and use a calculator (one that doesn't store steps) and tapped some keys ...
4answers
3k views

### 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\;...
2answers
2k views

### A moderate visual number puzzle

In the following diagram, each red dot represents a positive number. The dot-numbers on each of the five circles spell out either a word (each dot corresponding to a letter) or a number (each dot ...
4answers
2k views

### Sum other numbers

Begin with a flagrantly erroneous summation and a woefully vacant substitution table. 234 + 5 Digit 2 3 4 5 6 7 8 ------- ...
6answers
23k views

### The 10,958 Problem

Here is the task: Write down 10958 using all 1-9 digits in ascending order and only one time. You are allowed to: 1) group digits into numbers 2) use 5 basic operations: + - * / ^ ("^" ...
1answer
736 views

### A Tour Around a Triangle

Place the 18 even integers between 2 and 36 in the empty nodes of this triangular graph in such a way that if a path is drawn by coloring in red all the edges joining any two nodes whose numbers add ...
2answers
2k views

### Where is Jimmy's father? [duplicate]

(It's an old soviet math problem, no tricks or anything here) Jimmy is 21 years younger than his mother. Six years from now, Jimmy's mother will be five times as old as Jimmy. Where is Jimmy's ...
2answers
761 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 ...
4answers
775 views

### Consecutive integers around a circle

Find a block of positive consecutive integers that can be placed around a circle in some order so that any two adjacent numbers always have a common divisor greater than 1.
5answers
864 views

### Primes less than 100 in a 4 x 4 board

Place one of the digits (0 to 9) in each of the cells of a 4 x 4 board so that as many as possible of the 25 primes less than 100 divide at least one of 10 positive 4-digit numbers that can be read ...
1answer
493 views

### A partition of 1000 into nine parts

The sum of nine whole numbers is 1000. If those numbers are placed on the vertices of this graph, two of them will be joined by an edge if and only if they have a common divisor greater than 1 (i.e. ...
3answers
2k views

### A partition of 100 into nine parts

The sum of $9$ positive natural numbers, not necessarily distinct, is $100$. If placed appropriately on the vertices of the following graph, two of them will be joined by an edge if and only if they ...
7answers
9k views

### Make 24 using exactly three 3s

Make 24 using exactly three 3s Each number formed with a 3 and the 24 in the equation are all base 10. You cannot introduce any additional digits or constants. Plus(+), negation/subtraction (-), ...
2answers
920 views

### Buttons on an old non-scientific calculator are less sensitive

All 5 numbers are entered in an ascending order. These numbers are in an arithmetic progression. The value of the fifth number, i.e. the largest number, is less than 99. While adding these ...
1answer
746 views

### My Social Security Card Number

I have forgotten my social security card number. All I remember is that it is the largest integer with the property that the block of any two of its digits that are adjacent is either a two-digit ...
1answer
507 views

### Why you shouldn't buy cheap puzzle books

Backstory contains important information, but nothing hidden. Also, tl;dr parts are bolded, but I can't guarantee I didn't forget bolding some part. Recently there's been a grid-deduction craze here ...
14answers
3k views

### Yet another matchstick puzzle

Inspired by this post, here there is my attempt at a matches' puzzle. The expression 1 = 850 - 9 - 6 is obviously wrong: move exactly three matches to obtain a correct expression. Rules are: This ...
5answers
4k views

### My five daughters

The sum of the ages of my five daughters is 43. The ages of any two of them have a common factor greater than 1. How old are my daughters?
2answers
2k views

### My Three Children

The sum of the ages of my three children is 40. Though the ages of my two daughters are relatively prime (i. e. they have no common divisor), the age of each of them does have a common divisor greater ...
5answers
557 views

### 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 (...
3answers
775 views

### The Mxied Atdiiodn

It has been swohn that to raed a txet the oedrr in which the lrtetes of each idniaduvl word aepapr is not ipmotanrt, so lnog as the fsrit and lsat ltetres are the correct oens. This is not the case ...
1answer
1k views

### Primes in a Diamond

Label the vertices of this graph with numbers 1 to 16 in such a way that the edges between any two vertices whose sum and absolute difference are both primes are precisely the edges of a hamiltonian ...
1answer
833 views

### Poring Over the Numbers: A Hidden Message

I thank my lucky stars I'm able to write this to you. I spent a hefty percentage of my remaining cash at the courier's office and I want to underscore the importance of this communique. If a man comes ...
2answers
527 views

### KenKen Zen: A journey begins

Let us shy away from the materialistic opulence of 361- cell KenKen layouts (−9 to +9, squared).  Let us contemplate a modest KenKen journey, unburdened by gratuitously ...
7answers
3k views

### Longest arithmetic expression where the answer is equal to the number of letters

You can use any mathematical operations represented by English words. These English words must be found in a commonly used dictionary. Spaces are neither letters nor words. You can not use the same ...
3answers
1k views

### Four Marathon Runners

Four marathon runners, each identified with a positive whole number, sit around a table. Each of them notices that their own number has a common divisor with the number of the runner sitting on his ...
5answers
855 views

### Divisible Dates

The day of the month, and the month of the year, often simultaneously divide the year. Most recently it happened on January 3, 2019 because both 1 (January) and 3 divide 2019. In our era, since 1/1/...
4answers
1k views

### A Magic Diamond

Place 15 different positive integers on the vertices of this graph so that the ten products of three numbers in a straight line are all equal.
1answer
407 views

### Zero, One, Two, Three, etc

Find a solution to the following system of simultaneous equations. All letters stand for integers (positive, zero, or negative), and different letters are different integers. The preferred solution ...
1answer
551 views

### The Vacuumed Quotes

A colleague of mine likes to put his favorite quotes up on the fridge using those little magnetic letters. This morning the cleaner came and accidentally vacuumed up all the letters. We were able to ...
2answers
301 views

### How to fill a honeymoon

How can a honeybee visit all cells exactly once in this crescent shaped honeycomb, beginning at the bottom tip and ending at the top? The starting cell, at ...
5answers
427 views

### The oldest wins the prize, but they won't tell their age

I'm trying to design a problem that should be as close as possible to the following setup, while meeting some requirements about its solutions. Initial setup There is a group of more than 2 people ...
2answers
819 views

### A unique partition of 200 into 6 parts

The sum of six positive integers is 200. If placed appropriately on the vertices of this graph, two of them will be joined by an edge if, and only if, they are not relatively prime, that is, if they ...
3answers
413 views

### Sum self enumerated digits

Please fill in the entire summations for lines 4 through 9 and just the total for line 1,000,000.         1.     1   =   1   ...
1answer
130 views

### Products or sums

Arrange the integers between 1 to 20 on twenty of the cells of this board, precisely two on each row and each column. The sum or product of the two numbers in each row must be the number on its right, ...
1answer
279 views

### H-one-one-oneycomb

What path could a honeybee follow to fill all cells with honey, beginning and ending at the center and visiting every cell exactly once? At first the only ...
2answers
670 views

### Four Magic Ellipses

These four ellipses represent four sets and all the possible ways they can intersect (a Venn diagram, in other words). There are 8 regions inside each ellipse, and 15 regions altogether. Is it ...
3answers
601 views

### My forgotten PIN

I´ve forgotten my PIN, a four-digit number. All I remember is that it is a perfect square, and that it has at least one digit in common with every other four-digit square number. What is it?
1answer
343 views

### Little Red Solving Hood goes one-stop swapping

Moral of the story:   Two stored values may be swapped arithmetically with 4 or fewer variable references. Puzzle of the story:   Can you exemplify the moral?   (With 10 or ...
1answer
224 views

### A Tetrad Puzzle: Find The Key

I made this to test some ideas for a game I'm developing. Feedback would be appreciated. What is the key?
3answers
787 views

### Gaby and Jack's Number Guessing Game

Gaby, a good mathematician, thinks of a whole number between 1 and 100 inclusive. What is the least number of questions Jack needs to ask her, and what questions should those be, if he is to work out ...
2answers
571 views

### Primes and Squares

Place a different prime or square number on each of the fifteen disks below so that the number in any disk that lies on two others is the sum of the numbers in those disks. Do so in such a way that ...
2answers
946 views

### Videogame salesmen

Two gamers sell their collection of XBOX games. They've got as many Euros as there were games in the collection originally for each game. They split the money by having the first gamer take 10 Euros ...
1answer
966 views

### Aiming for the 24

6 1 3 4 = ?? Using four basic math signs (+, -, *, /) and brackets, for instance: 6 * (1 + 3) - 4 = 20 6 * 1 * 3 + 4 = 22 6 + 13 + 4 = 23 (6 + 1)* 3 + 4 = 25 61 - 34 = 27 Try ...
1answer
159 views

### My Sister's Six Children

My sister has six children whose ages add up to 40. The ages of any two of her three boys have a common divisor greater than 1, and so do the ages of any two of the ages of her three girls. However, ...
2answers
210 views

### Numbered Billiard Balls

Ten billiard balls are stacked in the form of a regular tetrahedron, six in the bottom layer, three in the middle layer, and one in the top layer or cuspid. All the balls are numbered (with positive ...
2answers
1k views

### Difficult sequence

Here I go : $3 + 5 + 6 = 15 \ 18 \ 72$ $5+ 5 + 6 = 25 \ 30 \ 94$ $5 + 6 + 7 = 30 \ 35 \ 85$ $5 + 5 + 3 = 25 \ 15 \ 73$ $9 + 4 + 7 = 36 \ 63 \ ?$ Replace ? with appropriate number