Questions tagged [no-computers]

A puzzle designed to be solved without using calculators, online decoders, or computer programming. Using a computer to type and post the answer is allowed; the spirit of this tag is to make people solve the puzzle on their own.

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7
votes
4answers
958 views

A Five City Loop, starting and ending in MA

Complete a loop of five large cities. The starting city name starts with the letters MA. Each of the following cities starts with the last two letters of the previous city name. (Like PARIS ISTANBUL ...
7
votes
1answer
758 views

Inequality derived from a famous problem

Let's have the following inequality: $\frac{2}{3}(\sqrt 5-1)^3\lessgtr\sqrt[3]{2}$. Which part is greater, the left or the right? No calculator solutions are accepted.
6
votes
1answer
551 views

Flat share share

This is a sequel to Gentrification in Chessshire. Due to the febrile state of the Chesster housing market you and your flat mates are forced to rent out half your place to another group of sharers. ...
3
votes
1answer
184 views

Quadruped Mosaic

This is a visual puzzle (known as "mosaic" or "fill-a-pix") with the same rules as MineSweeper: This puzzle has exactly 100 x 100 cells. The grid is to be filled with colored and ...
16
votes
1answer
764 views

What number goes in the ?? box?

A simple pattern puzzle What is the number in the ?? box? Why? No programming please.
-1
votes
1answer
88 views

Consecutive number division puzzle 2 [closed]

Find 4 consecutive numbers that divide 𝑤, 𝑥, 𝑦, 𝑧 respectively, where 𝑤, 𝑥, 𝑦, and 𝑧 are also 4 consecutive positive numbers greater than 1, or prove it's impossible. Bonus: What if w > the ...
5
votes
2answers
225 views

Wraps and Loops—Some Concrete Examples

This puzzle serves as the more concrete sequel to my previous post; in particular, see that post for the rules of the game. Rather than (implicitly) demanding a description of a polynomial-time ...
2
votes
2answers
298 views

Four Mathematicians, Four Poker Hands and Four Clues

These four mathematician friends play poker every Saturday night. They always have a twist for the very last hand, just for fun. This Saturday the twist was “Factorial Clues”. The rule for the last ...
7
votes
5answers
636 views

What a coincidence or eighteen is not seventeen take two

Since I botched my first attempt at posing this puzzle, let me try again, this time hopefully closing all loopholes by dropping the packing angle and making this a purely geometric puzzle: The figure ...
6
votes
2answers
2k views

Eighteen is not seventeen

This question is not the same as Adding coins inside a ring of coins From a pile of equal size perfectly round coins take eighteen and make a perfect ring. Show that you can fit at least sixteen more ...
12
votes
1answer
190 views

Wormeus and the Stickotaur (maze 3)

This is the third maze in the Wormeus series. Previous puzzles are here and here This shouldn’t be too difficult but contains a cute gimmick that isn’t possible in the original Theseus mazes sans the ...
3
votes
1answer
65 views

Divisors ending with digits 0-9 each

What is the smallest positive integer, which has - for each of the digit 0-9 - a divisor ending with this digit?
6
votes
1answer
209 views

A 3x3 grid with common factors

A $3 \times 3$ grid $G$ is filled with every number from the set $\{2,3,5,6,7,11,14,15,30\}$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that ...
11
votes
4answers
944 views

Deriving a 3x3 grid from another one

A $3 \times 3$ grid $G$ is filled with every number from $1$ to $9$. Now a new $3 \times 3$ grid $H$ is formed, such that $H_{ij}$ is the number of neighbors of $G_{ij}$ that are greater than $G_{ij}$....
0
votes
1answer
84 views

Self-indulgent numbers

Let's call a positive integer N self-indulgent of degree K>2 if for every positive integer k<K the following is true: More than half of the first k multiples N,2N,...,kN of N contain with ...
8
votes
1answer
314 views

Manual tiling with 8 dodecadudes

Here are 8 dodecadudes. (Drawn from the very numerous dodecadrafters, made from 12 half equilateral triangles, dodecadudes are a subset of 770 pieces with sharp points and narrow necks excluded). ...
8
votes
5answers
1k views

Split 1 through 6 into a product of 24 and sum of 12

How many ways are there to split the numbers 1, 2, 3, 4, 5, and 6 into two groups, such that the product of the numbers in one group is 24 and the sum of the numbers in the other group is 12? An ...
9
votes
1answer
164 views

Wormeus and the Stickotaur (maze 2)

Here is another Wormeus maze, following a previous puzzle that is yet to go viral. Wormeus has to eat all the apples without dying a horrible squishy death at the hands of the Pink Lady Stickotaur. I ...
11
votes
3answers
1k views

Swapping 3 knights in a 4x4 grid

Can you swap black and white knights in this 4x4 grid? There is one important constraint: at no point can a knight be under attack by an opponent knight. Knights move using standard chess moves (L ...
19
votes
1answer
613 views

Quartum non datur

Can you give a good rational approximation of $$\sqrt[3]2 \times \sqrt[4]2$$ without doing any significant maths? Hint: Attribution: Mine.
11
votes
2answers
328 views

Wormeus and the Pink Lady Stickotaur

Wormeus lives in a labyrinth containing lots of apples. His main ambition in life is to eat as many apples as possible but his nemesis, the evil Pink Lady Stickotaur, has other ideas – if you pardon ...
12
votes
1answer
364 views

AnaCross: A crossword made of anagrams

This is a new type of puzzle I've devised: the AnaCross. Nothing new under the sun and all, I'm sure someone has made one before, but I've never seen it. The rules are pretty simple. At the end of ...
2
votes
0answers
194 views

This ᴀɴᴅ That musical act from the past [closed]

Below is a fill-in-the-blanks three-part list of variously-venerable musical acts of the form “________ ᴀɴᴅ ʜɪs/ᴏᴜʀ/ᴛʜᴇ _________.” The example of “Paul Revere ᴀɴᴅ ᴛʜᴇ Raiders” has been filled in for ...
1
vote
1answer
172 views

Probability of a successful DT Cannon

In multiplayer Tetris, there are a number of opening setups that let you send powerful attacks very quickly. One popular opening is the DT Cannon, which allows the player to very quickly send a T-Spin ...
3
votes
1answer
155 views

Non-increasing arrangement

We are arranging the numbers from 1 to 8 in an order so that three consecutive terms cannot be increasing. For example, 12345678 isn’t allowed but 81436572 is. How many ways are there to do it? Please ...
19
votes
1answer
437 views

Escape from Sudoku!

An entry in Fortnightly Topic Challenge #50: Escape Rooms I hesitated to enter this in the Escape Room FTC, but I definitely was inspired by the challenge to create this puzzle, and it is, in some ...
4
votes
1answer
1k views

Find three ways of forming the number 100 using 3,3,5,7

As it says in the title. Rules: anything not explicitly allowed is forbidden. use 3, 3, 5, 7 and multiplication, division, sum, difference, unary minus, and exponentiation in any order. Parentheses ...
12
votes
1answer
207 views

Three white queens, two white knights, and one rook on a chess board

On an 8 x 8 chessboard, place three white queens, two white knights, and one white rook so that every cell of the board is under attack by at least one piece not standing on it. Source: https://www....
4
votes
1answer
146 views

Chess - I will eat!

Suppose that you are playing White, and your aim is to eat a black piece (pawns qualitfy) in the fewest moves as possible and Black are not cooperating at all, and, even more, Black's aim is to ...
13
votes
1answer
2k views

A Math Riddle: But the math does not add up

Grandpa had a lot of different books of stamps on his desk. He was counting them. I was curious. “What are all those stamps Grandpa?” “I just got back from the Post Office son and bought a bunch of ...
9
votes
1answer
394 views

Trivia… sudoku

An entry in Fortnightly Topic Challenge #49: Pub Quiz Camouflage Please do not search the answers online (hence the no-computers tag), otherwise it would be too simple to solve this puzzle. I tried ...
6
votes
2answers
337 views

Twin primes and divisibility

Let $p$ and $q$ be a pair of twin primes. Find the smallest possible value of $a+b$ where $a$ and $b$ are positive integers such that $p\;|\;(a+qb)$ and $q\;|\;(a+pb)$. This puzzle is my own ...
30
votes
5answers
5k views

How can 3 queens control the white squares?

It is well known that there is no way of arranging 4 queens on a checker board in such a way that every square is occupied or threatened. Now consider a slight variation where we only need to cover ...
10
votes
1answer
409 views

A Cryptic Cryptarithm

An entry in Fortnightly Topic Challenge #48: Unusual tag mix Solve these puzzles to reveal why I made them. Matriarch mostly prepared oats for American airline location? (8) AIRLINE + LOCATION = ? 51 ...
2
votes
1answer
79 views

Number conversion via Prime route

This is a variation of the Word Ladder. Instead this is a number ladder. Convert the number 12345 to the number 54321 in seven or less steps with the following rules A: You can only change any one ...
9
votes
1answer
268 views

Chess Endgame Study

I came across this puzzle-like endgame study. Usually, opposite color bishops are draw-ish. Here's an absolutely extraordinary counter-example. Enjoy! White to play and mate in 8. Source: Winning ...
0
votes
0answers
46 views

An orderly transition of power [duplicate]

Since it's the 20th of January, perhaps we can demonstrate an orderly transition from TRUMP to BIDEN? There are eight steps to get there and all words are found in the World Scrabble dictionary. One ...
7
votes
1answer
190 views

Three to Seven in five or less

Can you change the word Three to the word Seven in five steps or less with the following rules: You must exactly replace two letters; one vowel and one consonant of the word in each step with a ...
0
votes
0answers
92 views

First digit of 2021^2021 [duplicate]

Can you find the first digit of $2021^{2021}$ without a computer? Good luck!
8
votes
3answers
388 views

With a little effort, one can prevail

What is common between the following words and names? (Inspired by this except that I actually know the answer to this one) Defeat Kleenex? Guanaco Nerdiest Sardar Ian McKellen Dingo Gun Diablo ...
5
votes
3answers
330 views

A Circle of numbers

Just saw a Circle of numbers on my Whats App message (source not listed) which is as following Arrange numbers 1 to 32 in a circle such that any two adjacent (neighboring) numbers add up to a perfect ...
7
votes
1answer
501 views

A special number

Here is a nice puzzle from my friend. Can you find a number that is a product of two consecutive primes and when multiplied by its own reversal produces a palindrome? The answer may surprise you. No ...
8
votes
2answers
369 views

Rack 'Em Up! 🎱

In a game of English eight-ball pool, a set of 15 balls are arranged or 'racked' in the shape of an equilateral triangle. In order for the balls to be racked fairly, they must be arranged like so: <...
4
votes
1answer
145 views

Find the fastest stalemate for Black!

In the below position, how many moves will it take for Black to be stalemated? Black moves first, and both sides are working together. Black's pawns are moving down. Have fun solving! Zdravko Maslar, ...
6
votes
1answer
266 views

An Artistic Bunch

Luke, Clive, Anton and Paul are four talented creative artists, one a dancer, one a painter, one a singer, and one a writer. (Though not necessarily respectively.) Luke and Anton were in the audience ...
7
votes
2answers
1k views

I have a bad feeling about this country name

What is the longest country name that can be fully anagramed into one word from the Merriam-Webster dictionary? Please use this site for the list of countries. Minimum length 8 letters. If a country ...
7
votes
1answer
231 views

Expanding on a classic

From the simple caesar to the seemingly uncrackable elliptic curve, there are countless ways to obscure - and even hide - a sensitive message. Cryptography is quite interesting in this way. I find the ...
7
votes
2answers
341 views

Pentomino tiling on wrap-around 5x5 grids

It is known that P pentominoes cannot tile a 5x5 square board. Q1: If the east and west edges of the 5x5 square board are "wrapping around" (if you move a piece through one of the edges, the ...
2
votes
4answers
460 views

Crossing out every second number

Write down all integers from 1 to 1000. Cross out the first number and every second number after that. So you will cross out 1, 3, 5 and so on. Now repeat the process exactly - cross out the first ...
3
votes
1answer
212 views

n rows and 18 columns

I haven't posted for a long long time, so here is an interesting combinatorics problem! There is a table with 𝑛 rows and 18 columns. Each of its cells contains a 0 or a 1. The table satisfies the ...

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