# Questions tagged [arithmetic]

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

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523 views

### Table of mathematical expressions - fill in 1-9

Fill in the numbers 1 through 9 in the 9 empty cells (each number appears exactly once) to make the row and column expressions equal to the number at the end of the row or column. Regular math ...
102 views

### digits in descending order equals 2022

Happy New Year! Here's a nice puzzle for you guys. 2021 has started and can be written as $$(-9+8)*7-6*(5-(4+3)^{2+1})+0=2021$$ Ofcourse many other solutions are possible! So, the obvious puzzle is:...
139 views

### Four rational numbers whose product is 10 and whose sum is 0

It has been shown that every positive integer is the product of four rational numbers whose sum is 0. Thus: ...
231 views

### Addition table with hidden digits

Similar to the previous puzzle, find the values behind the letters. ...
241 views

### Yet another mixed sum

An instance of this puzzle is here: https://www.theguardian.com/science/2020/nov/16/can-you-solve-it-the-srcmalbed-nmebur-plzuze a) It has been swhon taht to raed a txet the oedrr in wihch the ...
98 views

### How do you find the sum of the digits contiguous to one which is situated in a three by three table?

The problem is as follows: I am placing the numbers from 1 to 9 in the squares of a 3 x 3 board. I start by placing the numbers 1, 2, 3 and 4 as shown in the figure. For the number 5, the sum of the ...
359 views

### Some mathematical magic

The magician will perform some mathematical magic. He asks his guest to secretly pick any two digit number and then perform a number of operations on it. If the number is even, divide by 2, if it is ...
599 views

### Chain Puzzle: Tabletop Games #05 - It's Yahtzee, Jim, but not as we know it

This is the fifth Chain Puzzle in the Tabletop Games series, in which all puzzles are themed around board games, card games, tile games, and the like. The answer to this puzzle is a thematic word or ...
106 views

### Find the mass of a specific weight given information about other groups

The problem is as follows: Vincent has 19 different calibrated weights whose weights are 1g, 2g, 3g, and so on up to 19g. Nine of them are made from steel, nine are made from brass, and the remaining ...
148 views

### Given pairs of weights find individual values

The problem is as follows: A kid has five marbles. These marbles have different weights and the child weighs them in pairs in all possible ways. He records the weights in his notebook. These are the ...
180 views

### Find the competition rankings of three people based on their final scores

I found this puzzle in my Logic and Reason book from 2000's. The topic is ordering information. From the looks of it seems to be an adaptation from a reprinted version of Martin Gardner's 70's book of ...
95 views

### Sum with letters, find the values

In the following addition setup, each letter correspond to a unique digit. Find the different values of the letters. Requirement: r is not equal to 0. ...
427 views

### The art of computer programming

EDIT: I know we are not supposed to edit in new requirements after first posting but as far as I understand it this requirement is implicit in all questions here: Explain your answer! At least a ...
109 views

### XOR -Is it possible to prove that if A=CāB then B=CāA and C=AāB using Boolean algebra only? [closed]

If you write out the truth tables then it's pretty simple but I was wondering if there was a nicer proof using Boolean algebra only
2k views

### 77-digit number divisible by 7 with seven 7s

The smallest number divisible by 7 with seven 7s is trivially 7777777. Then, what is the greatest 77-digit number divisible by 7 which contains seven 7s?
159 views

### How to get these outputs using these inputs?

Examples of inputs and outputs: Input: 3 7 20 Output: 1 Input: 17 2 1651 Output: 34 Input: 4 3 5 Output: 2 Input: 1000000000 1000000000 1000000007 Output: 49 Input: 27 37 100 Output: 99
165 views

-What is your password?- my niece asks me. -It is a four digit number. -I know that. -It is divisible by precisely three primes. -Tell me more. -It has at least one common divisor greater than 1 with ...
163 views

### How many steps for matchstick-Lychrel numbers?

The Lychrel number is famous in the recreational mathematics. The process about the Lychrel numbers reverses arrangement of the previous number. Mimicking Lychrel numbers, I would like to devise ...
348 views

### Remember the 60s? Far-out man!

Can you convert the following to my unusual currency? 1.25, 1.75, 2.75, 3.25 Having done that, can you explain why some people think the smallest of these is somehow the biggest - at least as far I'm ...
182 views

### What's one and one and one and one and [closed]

Good morning. Today I am going to test your mental arithmetic. To do so I shall ask you to give me the sum of a series of ones. I shall say One and one and one and one and one and one, etc. Of course ...
632 views

### The numbers on blackboard

The numbers $2020,2019,2018,...,1$ are written on the blackboard from left to right. John repeats the following process until there is only one number left: John chooses the first two numbers from ...
186 views

### Swapping the first and last digits of an integer

Take any n-digit integer (n > 1) and interchange its first and last digits. If neither of these is 0, and they are different, does it happen infinitely often that the resulting number is a multiple ...
445 views

### Pairs of Bogotá Numbers

A BogotĆ” number is a positive integer equal to some smaller number, or itself, times its digital product, i.e. the product of its digits. For example, 138 is a BogotĆ” number because 138 = 23 x (2 x 3)....
6k views

### 9-5=5? Matchstick problem

Move one matchstick to make an equality. Question made by me (Is this too easy?)
690 views

### A Covid-19 puzzle: Alcohol for your School!

You are the principal of a primary school in HK. Schools are resuming soon, and you have to ensure that your school have enough alcohol. Each of the 30 classrooms should have a bottle containing 500mL ...
131 views

### Numbers Relation Puzzle

I've written a numbers relation puzzle, I'd like to share it with you and see what you fellas think. ------ Try to find the relation between the numbers------ Good to know: there are 2 parameters ...
753 views

### Smallest integer whose first n multiples contain the digit 1

For some time now I have been investigating the function $M(n)$, the least integer such that the first $n$ multiples of $M(n)$ contain the digit $1$. Thus $M(3) = 51$, because $51$ is the smallest ...
1k views

### Confusion on a math puzzle

One of my colleagues asked me below puzzle, Three friends went to a picnic. 1st and 2nd friends collected woods for cooking where 3rd friend did not participated because he was sick. 1st friend ...
191 views

### The death prism

One day, you are caught by a evil wizard. He presents you with a prism, and says, "You can ask me to turn this prism to any $n$-angled right prism. Then you shall fill in $1$ to $3n$ with no ...
33 views

### Use all of the following symbols and numbers in one equation for the result to be equal to 10 [duplicate]

Use all of the following symbols and numbers in one equation for the result to be equal to 10 (14, 12, 9 , 7, 3) (Ć· Ć - +)
211 views

### Make the numbers 1-100 using 8 8s

Rules: Make the numbers 1-100 using eight 8s Use the operations + - * / exponentiation and ! No Rounding as in $(\sqrt{88}+8*8+8+8+8)/8= 12$ No using other digits Multi digit numbers ...
190 views

### Make the numbers 1-100 using six 6s

Rules: Make the numbers 1-100 using six 6s Use the operations + - * / exponentiation and ! No Rounding as in $((6 - (6 + 6) / 6) + 6!!) / 6 = 9$ No using other digits Multi digit ...
127 views

### What could be the answer of this maths puzzle? [closed]

Found this puzzle online. Tried many possible combinations of numbers with multiplication, addition etc. Has anyone ever solved this?
261 views

### NineFind - Which 9 Numbers Are Correct?

Text Version: ...
327 views

### Make the numbers 1-50 using the digits 2, 0, 2, 0

Try to make all the numbers from 1-50 using 2, 0, 2, 0 exactly once. Rules: Use only the operations +, -, *, /, !, exponents and square root No rounding eg. ...
449 views

### Can you decipher these ancient numerals?

This stone was found at the foot of an ancient door. This old note with some mathematical relationships was discovered nearby. Can you use this information to figure out what number each of the 9 ...
271 views

### Missing numbers

The hexagon below is almost complete but there are 3 missing numbers. Try replace the question marks! Hint Hint2: Hint3
422 views

### Find the missing number from the pyramid

? 1 3 3 3 9 9 3 1 9 Find the missing number in the pyramid?
304 views

### Catching the thief before it's too late

London, 17:15. Inspector Arbor wasn't quite happy with the current situation. Normally, he would have enjoyed this sunny Saturday outside at the Park but now wasn't the time for that. Valuable ...
720 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 ...
233 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 ...
299 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 ...
99 views

### Highest scoring words based on distance travelled along the alphabet v2

This is a follow on from my previous word puzzle: Highest scoring words based on distance travelled along the alphabet The twist in this puzzle which opens it up a lot more is that the alphabet can ...
460 views

### Highest scoring words based on distance travelled along the alphabet

For any word we define it's alphabetic distance to be the total amount of places in the alphabet you need to traverse between each letter. Example: WORD has a score of 25 8 character distance ...
161 views

### Free Assignment: Longest Word Worth a Million

This is very much inspired by this question. Take the first 26 primes and relate each one to a letter of the alphabet. On this occasion, you may choose how each number is mapped to each letter (...
364 views

$(A)72$ $(B)18$ $(C)9$ $(D)19$ Source:My coaching DPP The question asks you identify the pattern and find the missing character. I have been trying to solve this problem from a long time but I ...
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 = ...
224 views

### How do I solve this problem?

I am trying to answer this puzzle - which of the five potential answers is correct, and why? This test comes from Metropol iq1 book