# Questions tagged [arithmetic]

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

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### 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 ...
17k 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 ...
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 ...
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 ...
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\;...
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 ...
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 ------- ...
1k views

### What is a BEN Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a BEN Number™. Use the following examples ...
25k 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: + - * / ^ ("^" ...
762 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 ...
874 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.
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 ...
777 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 ...
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 =...
958 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 the 10 positive 4-digit numbers that can be ...
505 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. ...
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 ...
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 (-), ...
932 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 ...
760 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 ...
550 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 ...
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 ...
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?
639 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 (...
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 ...
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 ...
272 views

### Happy birthday Ramanujan!

On December 22 2019, Ramanujan would have been 132 years old. In his memory here are two puzzles around 132. In the six vertices of each of these graphs place six positive integers that add up to ...
779 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 ...
454 views

### 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 ...
845 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 ...
531 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 ...
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 ...
2k 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.
466 views

### What is a Heptagon Number™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with Number version puzzles. If a number conforms to a special rule, I call it a Heptagon Number™. Use the following ...
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 ...
205 views

### One Step Forward, Two Steps Back

What is the next number in this never-ending sequence? 0 1 1 110 111 101 11000 11101 10101 1100110 1001011 ...
862 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/...
593 views

### A Magic Flying Saucer

Place 19 different positive integers on the vertices of this graph so that the 13 products of three numbers in a straight line are all equal. Do so in such a way that the product is as small as ...
412 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 ...
258 views

### What is a Commutative Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles. If a word conforms to a special rule, I call it a Commutative Word™. Use ...
555 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 ...
308 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 ...
3k views

### Longest word worth at most a million

An old and popular puzzle, recently revived on Twitter by Alex Bellos, Chris Smith, and others, asks to take the first 26 primes, relate each to letters of the alphabet (A = 2, B = 3, C = 5, ..., Y = ...
447 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 ...
830 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 ...
435 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   ...
288 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 ...
678 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 ...