# Questions tagged [arithmetic]

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

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476 views

### Number Equation Matrix

Can somebody please solve this? My daughter's school teacher gave her this puzzle to solve at home. But to me it seems a little out of order, and that's why I am asking here for help.
217 views

### Primes from arithmetic and geometric progressions

The five primes, 131, 157, 211, 349, 739, are neither in arithmetic or geometric progression, but are instead the sum of the corresponding terms of two progressions of five terms each, one arithmetic ...
251 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 ...
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 ...
445 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 ...
584 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 ...
152 views

### Rearrange these 9 digits - combinatorics puzzle

4 3 2 7 1 9 6 5 8 Can you rearrange these 9 digits so that in all of the 8 directions the difference between one of the digits and the sum of the remaining two shall always be the same? In the ...
910 views

### What is a Finale 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 Finale Number™. Use the following examples ...
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 ...
169 views

### Find the number that does not fit into the pattern shown below

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 12 34 56 78 910 1112 1314 1516 1718 1920 2122 2324 2526 2728 2930 3132 3334 3536 Each row forms a set which implements a pattern. The two patterns ...
925 views

### Big number puzzle

I saw this on rec.puzzles many years ago, but can't find the reference to credit the source. I am thinking of a large number. If you want to multiply it by a two digit number $ab$ with $a \lt b$, ...
260 views

### What is a Valid 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 Valid Word™. Use the ...
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.
586 views

### What is a Trio 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 Trio Word™. Use the ...
14k views

### Make numbers 1-30 using 2, 0, 1, 9

This is very similar to the 2, 0, 1, 8 problem. Just try to make all numbers 1-30 using the digits 2, 0, 1, 9. Rules: Use all four digits exactly once Allowed operations: +, -, x, ÷, ! (factorial), ...
362 views

### Is it True that Two + Two = 2? If so, what is Ten + Ten and Nine + Nine?

Given: SIX + ZERO = 4 TWO + THREE = 15 FIVE + SIX = 88 ONE + TWO = 83 TEN + TWO = 13 If so, is TWO + TWO = 2 correct? What is TEN + TEN ? NINE + NINE ? Hint 1
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 (-), ...
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 ...
127 views

### Express the Squares of first 20 Numbers with only numbers found in their Sum of Digits

Allowed Operations ...Addition, Subtraction, Multiplication, Division, Exponentiation, Simple Factorial. Left and Right Brackets allowed. Expression should involve minimum number of total characters: ...
173 views

### Standard Sudoku Specialized with just 2 Primes

A standard 9x9 Sudoku uses the digits 1 to 9. You are only allowed two distinct primes to represent 1 to 9. Find out the minimum number of characters (digits + signs) needed to construct a Sudoku ...
143 views

### Numberless Sudoku with Just a Letter and Symbol Combination

A Standard 9x9 Sudoku uses the digits 1 to 9. You are only allowed to use a single letter(say T) and a symbol of your choice to represent the digits 1 to 9. Rules should be well defined and the ...
88 views

### Make N N N equal to 6 where N is 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 [duplicate]

Using standard mathematical symbols, (i.e. no other letters or numbers), make the following true: ...
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 ...
868 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 ...
82 views

### Cross-number of two, three and four-digit numbers

In this cross-number two-digit numbers are prime numbers, three-digit numbers are square numbers and four-digit numbers are palindromic numbers.
1k views

### Father and Son and Grandsons

The sum of the ages of a father, his son, and his two grandsons is 181. The father´s age has a common divisor greater than 1 with the ages of each of his three descendants, but not two of the latter ...
408 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 ...
811 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.
524 views

### 1 0 1 0 1 0 1 0 1 0 1

Start with the digits:       $1\ 0\ 1\ 0\ 1\ 0\ 1\ 0\ 1\ 0\ 1$ You may then add (only!) these simple arithmetic operators:       $+\ -\ \times\ \div$ You may also ...
103 views

### Pairwise coprime numbers in a 3 x 3 board

Find all the ways of placing all the digits 1 to 9 in the cells of a 3 x 3 board in such a manner that the seven three-digit numbers that can be read horizontally (from left to right), vertically (top ...
611 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 (...
170 views

### Making Branko Grünbaum's symmetrical 5-set Venn diagram magic

Place integers 1 to 31 in the 31 regions of Branko Grünbaum's symmetrical 5-set Venn diagram so that the sum inside any of the 5 sets is the same.
574 views

### Do the maths to call my name

My first one is my length. My second one is a bit closer to my third one than to my first one. My third one is my first and second together. My last one is four times my first one. ...
267 views

### Create all numbers from 1-100 by using 1,3,3,7

Create all the numbers from $1$ to $100$ using the numbers $1,$$3,$$3,$ and $7.$ You can only use each number once, except for the $3,$ of which you have two. You can use addition $(x+y),$ ...
856 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/...
232 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?
554 views

### Help solving a math puzzle table

I am struggling to find the answer. Here is the source: math logic puzzle phone app.
145 views

### From 2019 to digits

Is it possible to obtain the digits from 0 to 9 starting from 2019 and using its digits in the same order, together with the usual operations +, *, -, /, concatenation of digits, and the less usual ...
667 views

### Brain Testing Logical Reasoning Puzzle

Can you answer this logical puzzle? Puzzle Source: https://www.funwithpuzzles.com/2018/12/brain-testing-logical-reasoning-puzzle.html
790 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 ...
313 views

### A partition of 80 into seven parts

The sum of seven positive integers, not necessarily distinct, is 80. If placed appropriately on the vertices of this graph, two of them will be joined by an edge if and only if they have a common ...
776 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 ...
676 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 ...
581 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 ...
73 views

### Fly flight estimation [duplicate]

John and Peter are two friends living in two nearby villages 15km apart. One day they arrange to meet, but little do they know, a “flies marathon flyer”, an irritating fly, decides to play a game. ...
328 views

### The Magic Letter H

Place seven different positive integers on the empty disks of the H figure below so that the product of the three numbers in any straight black line is always the same. Now place seven other numbers ...
220 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 ...
750 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 ...