Questions tagged [arithmetic]

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

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10
votes
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.
6
votes
2answers
810 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 $a \lt b$, ...
4
votes
2answers
544 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 ...
2
votes
10answers
12k 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), ...
3
votes
2answers
359 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
15
votes
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 (-), ...
12
votes
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 ...
2
votes
3answers
120 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: ...
5
votes
2answers
166 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 ...
-5
votes
2answers
137 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 ...
1
vote
2answers
86 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: ...
73
votes
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 ...
18
votes
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 ...
5
votes
1answer
80 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.
6
votes
2answers
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 ...
10
votes
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 ...
19
votes
4answers
774 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.
3
votes
2answers
515 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 ...
2
votes
1answer
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 ...
12
votes
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 (...
3
votes
1answer
165 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.
6
votes
1answer
572 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. ...
1
vote
5answers
257 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 $(x+y),$ ...
10
votes
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/...
8
votes
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?
2
votes
1answer
381 views

Help solving a math puzzle table

I am struggling to find the answer. Here is the source: math logic puzzle phone app.
1
vote
1answer
139 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 ...
-3
votes
2answers
522 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
7
votes
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 ...
6
votes
2answers
294 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 ...
12
votes
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 ...
8
votes
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 ...
7
votes
2answers
570 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 ...
2
votes
1answer
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. ...
6
votes
2answers
320 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 ...
7
votes
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 ...
14
votes
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 ...
20
votes
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 ...
9
votes
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, ...
1
vote
2answers
129 views

Sums or products

Place the numbers 1 to 12 on twelve 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, while the ...
4
votes
2answers
863 views

Use 2, 0, 1 and 8 to make 71

Use all and only the digits $2,0,1,8$ once each to make the number $71$. Allowed operations; anything not on this list is banned: $+,-,\times,\div, ()$ (parentheses and/or choose function) ...
3
votes
1answer
136 views

make a sum with cards

Take the numbered diamond cards in a standard deck, that is those from 2 to 10. You may use some of them to form a sum: for example 23+45=68. What is the maximum result you may obtain? I hoped there ...
7
votes
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 ...
4
votes
1answer
161 views

A special square

Is there a four-digit square number which has at least one digit in common with every other four-digit square?
7
votes
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, ...
17
votes
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. ...
13
votes
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 ...
22
votes
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 ...
6
votes
1answer
348 views

Six sisters on the ski lift

The sum of the ages of six sisters known to me is 92. Though there is no single whole number greater than 1 that simultaneously divides the ages of any three of them, I did notice this morning, while ...
26
votes
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: + - * / ^ ("^" ...