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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6
votes
1answer
129 views

Tiling three pears with three-pair hexominos

The 21 hexominos below are all those that can be made by joining three dominos together (i.e. they have a perfect matching with respect to the graph of their squares) and are not rectangles. The ...
5
votes
1answer
119 views

White to play and mate in 3 - adapted from real game

This is adapted from a real game between GMs where white played the King's Gambit. I changed the position slightly (moved one piece) because there were actually two mates available, with one more ...
-7
votes
1answer
98 views

Puzzling rectangles [closed]

Can you find two unequal rectangles whose areas add to $5\sqrt5$? No computer solutions please.
9
votes
3answers
721 views

Heteropalindromes in a Word Square

Say hello to a not-so-simple, 4x4 word square: This little monstrosity has two rules; to define the first rule, have you ever heard of a heteropalindrome? Strings of letters that form words when ...
0
votes
1answer
146 views

How do I ring my friend's doorbell?

My friend, a curmudgeon who dislikes visitors, recently installed a puzzle-doorbell. It consists of ten push buttons in a row, labelled from left to right: ...
19
votes
3answers
2k views

The Thieves and the Gold Bars

Two thieves (Rod and Lia) carry out a big heist and steal 16 gold bars. They get away in their car when they run into a bad accident and the car is completely wrecked. Luckily they survive with their ...
3
votes
2answers
735 views

Most points on a circle

What is the most number of integer lattice points that lie on the circumference of a single circle whose radius is 80 or less? Please no computer computations.
6
votes
1answer
1k views

Life, uh, Finds a Way

[Rated PG-13 for language} I saw someone wearing a "Life happens" t-shirt, which is a fine enough sentiment, but not the most common turn of phrase. It made me wonder... How fast can you ...
30
votes
2answers
3k views

Sum of the first 86 square roots

Without using a calculator or a computer, can you compute the sum of square roots of the first 86 natural numbers, rounded to the nearest integer? In other words, we are looking for $\sqrt{1} + \sqrt{...
22
votes
3answers
1k views

Knight tour on a racetrack

Help the chess knight complete four clockwise laps on this racetrack, so that he lands on every square and never lands on the same square twice! The final square the knight lands on will be the same ...
4
votes
2answers
224 views

Seven 2s with seven math operations

Linked to A four digit number using exact same 4 digits A number with same repeated digits is called a Repdigit or Monodigit number https://en.wikipedia.org/wiki/Repdigit Can you write an equation for ...
5
votes
1answer
331 views

Hero Worms and The Minotaur

And so, Wormeus had a great time, eating every apple in sight, surviving several close calls with the Pink Lady Stickotaurs, respawning after the occasional horribly squishy death, exploring different ...
8
votes
1answer
178 views

Going off on multiple tangents

Given two disjoint circles of diameters D1 and D2 draw all shared tangents. Find the intersection points of all pairs of tangents. Discard those collinear with the two circle centre points. Of the ...
8
votes
2answers
498 views

Triangles to diamonds

Given a triangle ABC with sides a=|BC|,b=|CA|,c=|AB| a diamond is circumscribed around the triangle's incircle. The diamond and the triangle share the corner C along with (part of) sides a and b. ...
1
vote
1answer
110 views

Can you pick up an extra shift?

I was going through some old documents the other day and found some instructions for a one way cipher: Given a word w, iterate over its characters. For each character c, determine if its zero based ...
13
votes
6answers
4k views

A four digit number using exact same 4 digits

ABCD is a 4 digit number where A,B,C and D are 4 distinctly separate digits between 1 and 9. Using any of the following math operations and the digits A,B,C and D exactly once get the number ABCD. ...
6
votes
1answer
114 views

Wormeus and the Multiple Stickotaurs (Part 2)

This is the sixth puzzle in the Wormeus series and the second puzzle involving multiple Stickotaurs and wormhole puns. Wormhole-pairs are indicated with light green lines (note that this was ...
10
votes
2answers
601 views

When was Ensquare born?

Professor Matlogic posed this question to his smartest math student: "Famous mathematician Ensquare was born on this day, this month and this year AD at this time (hour and minutes) pm. True to ...
6
votes
1answer
781 views

Three cups and a ball

I am walking down the streets of Paris when a street performer approaches me. He has a row of 3 cups facing down on a table. He places a ball under the left cup. He proceeds to swap pairs of cups, ...
5
votes
1answer
160 views

Wormeus And The Multiple Stickotaurs

Here is the fifth maze in the Wormeus series. This time Wormeus is faced with multiple Stickotaurs and multiple Universes. Different universes are connected via … wait for it … drum roll ...
8
votes
3answers
2k views

Changing WATER to STEAM

How do you change the word Water to the word Steam by changing one letter at a time? The newly formed words must be from Merriam Webster dictionary. No proper nouns, abbreviations or acronyms. No ...
7
votes
1answer
283 views

AnaCross II: it's bigger now

So, I've prepared another AnaCross puzzle. The rules are exactly the same: At the end of each row is a pool of letters; those letters are the letters that go in that row of the crossword. Normal ...
4
votes
2answers
190 views

Cyclic squaring

Find a complex number $a$, which satisfies the following conditions: If you square $a$, you get a different complex number $b$. If you square $b$, you get a complex number $c$, which is different ...
7
votes
4answers
970 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 ...
8
votes
1answer
780 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
571 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
203 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
776 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
89 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
240 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
319 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
647 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
202 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
79 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?
7
votes
1answer
221 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
950 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
89 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
341 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
173 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 ...
12
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
631 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.
12
votes
2answers
433 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
436 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
198 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
232 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
159 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 ...
20
votes
1answer
478 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 ...

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