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Questions tagged [arithmetic]

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

3
votes
1answer
131 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
560 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. ...
63
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 ...
7
votes
2answers
186 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 (...
1
vote
5answers
214 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
785 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
200 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
186 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
127 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 ...
7
votes
3answers
772 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 ...
-3
votes
2answers
236 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
6
votes
2answers
256 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
767 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 ...
7
votes
2answers
561 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. ...
8
votes
2answers
647 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 ...
6
votes
2answers
279 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 ...
6
votes
2answers
197 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 ...
13
votes
1answer
729 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 ...
19
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
127 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
739 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
2answers
127 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
964 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
156 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
151 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, ...
22
votes
1answer
715 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 ...
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 ...
17
votes
1answer
471 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. ...
11
votes
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 ...
1
vote
8answers
5k 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
1answer
112 views

Calculate cost of excess water consumed [closed]

100 Liters of water is available equally in a month for consumption among 5 members @ 1 dollar per liter. If some members don't use their own available 20 liters, it can be used by the others at the ...
16
votes
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 ...
5
votes
5answers
400 views

The mathematical quiz

There are 4 equations. What should I put in place of the ? in the last one? 1 + 4 = 5 5 + 3 = 11 7 * 7 = 61 10 - 1 = ?
3
votes
5answers
584 views

Curiosity of February 5$^{th}$

Some people write February 5$^{th}$ using the md format, as $2.5$ or alternatively as $2/5$. Note that $2.5 \times \frac25 = 1$. Is there any other date satisfying $a.b \times \frac{a}{b} = 1$? ...
6
votes
1answer
338 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 ...
8
votes
3answers
541 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?
13
votes
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?
9
votes
2answers
776 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 ...
0
votes
2answers
193 views

Continue sequence

Son asked such a task. Continue the number sequence 5, 7, 8, 12, 11.... The son is in the second grade. They studied the operations of addition, subtraction and ...
6
votes
1answer
458 views

How many multiplications to find n^k given n, for general k?

I was looking at the nice puzzle Find $n^{23}$ with the least multiplication. My first instinct for this would have been to find $n^{2^i}$ for each $i$ first and then multiply these together as ...
7
votes
2answers
943 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 ...
14
votes
1answer
465 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 ...
4
votes
1answer
163 views

Turn based Number game

You and a friend take turns saying positive integers greater than one. You can't say a number that is a multiple of previous numbers or a sum of multiples of previous numbers. For example, if A says 3 ...
3
votes
2answers
155 views

Complete the equality (medium-hard)

Complete the equality to make it true: 1 1 1 1 1 = 945 Using similar logic, solve for this: 1 1 1 1 1 = 80 Info: You should ...
4
votes
4answers
276 views

Complete the equality

Complete the equality to make it true: 1 1 1 1 = 5 You can add any math operation or symbol to the left side. You cannot change right side nor the ...
4
votes
1answer
135 views

Remove two digit/symbol to find equality

Find the equality by removing any two digits or symbols (of course, except equal sign) $4\div3+63=9-23\times7\div3$ For example, if the equation below was given, Example: $91-81=45+12\div3-85$ ...
15
votes
2answers
913 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 ...
26
votes
6answers
17k 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: + - * / ^ ("^" ...