# 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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### Largest sequence of adjacent numbers less than 11 such that adjacent number divides the other

Friday writes different positive whole numbers that are all less than 11 next to each other in the sand. Robinson Crusoe looks at the sequence and notices with amusement that adjacent numbers are ...
• 3,101
1 vote
196 views

### A 3 digit perfect square and its reverse are both perfect squares. What is the number?

A three-digit perfect square number is such that if its digits are reversed, then the number obtained is also a perfect square. What is the number? For example, if 450 were a perfect square then 054 ...
• 3,101
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### Long Division when it is almost, but not entirely, wrong

Hmm, my last long division puzzle (Reconstruct a long division given less than a quarter of the digits, and all of those are wrong) didn't last the night. So let's try to make it harder. All of the ...
• 912
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### Reconstruct a long division given less than a quarter of the digits, and all of those are wrong

Inspired by "The Puffin Book of Brainteasers" I decided to try my hand at creating a long division missing digits problem where all of the displayed digits are wrong. On searching I found ...
• 912
2k views

### Can you color the 8x8 grid red and blue?

Consider an 8x8 grid made up of 64 unit squares. The goal is to color the 64 squares red or blue so that the following two constraints are satisfied: ROWS: For every pair of adjacent rows, exactly ...
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### Split a number in half, sum it, square it and get the number back

The number 3025 when split in the middle gives us 30 and 25. 30+25= 55. The square of 55 is 3025. What other 4 digits numbers have this property i.e. when the 4 digit number is split in the middle, ...
• 3,101
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### Keys and Locks Puzzle

Let $a,b,n$ be positive integers in which $a,b\le n$. You are locked in a room, with $n$ distinguishable keys and $n$ distinguishable locks in it. You know that each lock can be unlocked by a unique ...
• 5,924
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### Current record for minimally clued 7x7 Hidato (16 clues)

Background Back in March, I posted this question on the Puzzling Stack Exchange asking how many clues were needed to create a 4x4 Hidato puzzle with a unique solution. Sometime after this, I took a ...
• 2,413
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### Oh no, my chocolate banana puzzles are not unique!

There is a hidden message (7, 2) inside the solutions of the nine puzzles. An answer will only be accepted if it correctly identifies said message. Here are the Chocolate Banana puzzle rules. Each ...
• 3,185
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### Create an empty 8x8 One Up puzzle with a unique solution

Rodolfo Kurchan created a wonderful new grid puzzle called One Up that you can play on his website. There is one main rule: Each horizontal and vertical sequence of N cells between walls, must contain ...
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### Themed 7x21 Chocona

Chocona rules differ from Chocolate Banana rules. There is a hidden message inside the solution of the puzzle. An answer will only be accepted if it correctly identifies said message. The message is ...
• 3,185
196 views

### Themed 13x9 Chocolate Banana

There is a hidden message inside the solution of the puzzle. An answer will only be accepted if it correctly identifies said message. P.S. I promise this is my last Chocolate Banana puzzle of the ...
• 3,185
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### Prime and Composite 6x6 Chocolate Banana

The number of chocolates (black regions) is prime. Normal Chocolate Banana rules apply. Rules: Paint some of the cells black. Black cells linked orthogonally must always form a rectangle (or a ...
• 3,185
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### 9x13 Chocolate Banana Puzzle $\pi=\frac{43}{3.7^2}$

Since 37 is my favorite integer and π is my favorite number, here's another puzzle: Normal Chocolate Banana rules apply. Rules: Paint some of the cells black. Black cells linked orthogonally must ...
• 3,185
269 views

### 11x13 Chocolate Banana Followup

Your goal is to maximize the absolute difference of the numbers marked ?. (? marks indicate region areas. They may or may not ...
• 3,185
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### 10x10 Choco Banana

Normal Chocolate Banana rules apply. Rules Paint some of the cells black. Black cells linked orthogonally must always form a rectangle (or a square). Non-blacked cells linked orthogonally must not ...
• 3,185
376 views

### The game of 42: 10 cards to make 42

This is a game inspired by other recent questions. It is a 2-player game. The game is played with 10 cards numbered 1 to 10 and 2 positions or stacks. The game starts with all cards in stack 1. The ...
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### 4×6 Rectangle With A Twist

It is known that a $4\times6$ grid can be colored with two colors such that no four cells of the same color form an axis-aligned rectangle. The only valid coloring, up to permutation of its columns, ...
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### Which expression is larger?

Without using a calculator/computer, please show steps to determine which expression is larger: $(2^{90})!\quad vs.\quad2^{30!}$
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### Minimally clued 4x5 Hidato (4 clues)

Puzzle attribution: Me :) Background So as you might or might not know, I have been studying the minimum number of clues needed to force a unique solution in Hidato for variously sized boards. I ...
• 2,413
801 views

### Interesting equation with fractions

Find distinct positive integers $a$, $b$, $c$ and $d$ such that $$\frac{1}{a}+\frac{1}{b}+\frac{1}{c}-\frac{1}{d} = \frac{1}{a} \cdot \frac{1}{b} \cdot \frac{1}{c} \cdot\left( -\frac{1}{d}\right)$$ No ...
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### Invalid Jigsaw Sudoku Layout

The Jigsaw Sudoku Layout below is invalid (no Latin Squares exist for it). Why? Please find a short, yet complete, explanation (no computations involved). ...
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367 views

### Place numbers 1 through 9 in boxes (☐☐×☐=☐☐+☐☐=☐☐)

So recently I was scrolling through Youtube when I came across this video from MindYourDecisions that was about solving a legendary math puzzle. The puzzle: Place the numbers 1 through 9 in the ...
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### What Language Is This?

It is the year 2204, and we have finally found intelligent extraterrestrial life. We are delighted about this, so we asked the aliens, ...
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### Mate-in-25 tsumeshogi

This is apparently the first shogi-related question on this site! Yay! Anyway, this is a mate-in-25 tsumeshogi. Sente (the player with the pieces pointing up) is to move and by an uninterrupted series ...
• 7,720
956 views

### Anyone Seen My Snorkel?

This is part 54 of the puzzle series Around the World in Many Days. Each part is solvable on its own. mqoı ugw7qж , zqv qw o h6ım v6ınɔ ugwo7 | zo 78վn £þxm εıqm conxnøqxw v8կox h6ımw , დnɔ þn 7დvn ...
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### Hardcore Lighting - Excalidraw

Each yellow cell is a light that shines in exactly one direction, horizontally, vertically, or diagonally, endlessly, and goes through any block as long as the block is not a wall. Black cells do not ...
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### Why does the grid look different?

Relatively easy puzzle: Why does the grid look different?
• 3,185
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### Surely it's not Sny again

Each dot is a light, which shines in exactly one direction, horizontally, vertically, or diagonally (like a bishop, in a 45-degree angle). Lights shine through each other. Uncover the secret message ...
• 3,185
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### 7 Lights in 7 Tetrominos

In each orange tetromino, place a light that shines in all directions horizontally and vertically. Light shines through tetrominoes. Tetromino tiles are considered unlit initially and may be lit. ...
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### River crossing cats and dogs

A farmer and his $n$ cats and $m$ dogs are on one side of a river. There is a boat that can carry the farmer and at most $k$ animals at once. The boat doesn't move without a person operating it. The ...
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### Math is Awesome

I have a shirt. It says that $AWE+SOME=MATH.$ A, W, E, S, O, T, M, and H are not necessarily distinct positive integers from $0$ to $9$. The goal is to find the maximum possible value of $MATH.$ If ...
• 469
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### Pawns and a chessboard with no three aligned

This little problem crossed my mind and appeared to be not quite trivial. How can you place P pawns on a chessboard with the constraint that no pawn is exactly midway between two other pawns? Sure ...
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91 views

### Another hand tiling puzzle - 8 convex shapes from 7 polyiamonds

Arrange the 7 polyiamonds in the image into 8 different convex shapes. One after the other, not simultaneously... Rotating and flipping allowed. No gaps or overlaps. Should be a fairly easy puzzle.
• 4,108
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### Hand tiling polyiamond puzzle. Non-trivial

Group these 30 polyiamonds into five sets of six, then use each set of six to make five different convex shapes. There are some repeated polyiamonds, no set of six may contain a duplicate. The convex ...
• 4,108
266 views

### Constructing 2024 from the first 7 natural numbers

Can you use each number 1, 2, 3, 4, 5, 6, 7 exactly once, the four operations +, -, *, / and the parentheses to construct the number 2024? Bonus: can you find multiple distinct solutions? No computers ...
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246 views

### First five digits of a googol factorial

Based off of: MacPOW 1134 Without using a calculator/computer, can you determine the first five digits of $10^{100}!$ (a googol factorial)? I came up with this when trying to solve the question this ...
• 2,413
123 views

### Make three different convex shapes with four polyiamonds, by hand. Five times

To while away the endless holidays. Start with the four polyiamonds in row one. Arrange them without gaps or overlaps (flipping/rotating allowed) in a convex shape. Repeat for two more convex shapes, ...
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You are a mom (or dad) with two boys, Stephen and Philip, aged 8 and 10. While you have been out in the garage, they have been in their separate rooms doing their homework before being allowed to play....
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### Best Wishes for 2024: Four empty Suguru (Tectonic) puzzles

To continue last year's tradition, hereby four empty suguru puzzles. Rules of suguru: Each square gets a number so that each block of n squares has the numbers 1..n, and neighbouring squares (...
• 1,445
645 views

### It ended with an AFTERSHOCK

I started with a single-letter English language word. At each step, I added a letter of my choice, then re-arranged the letters to make a new word. I ended up with: AFTERSHOCK How did I get there? ...
• 512
355 views

### Add as few plus signs as possible to make equation true

To allow new users to solve this puzzle and earn reputation points, I encourage all users whose reputation is 200 or more to not post an answer until 48 hours after this question is posted. Thank you! ...
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### PSE Advent Calendar 2023 (Day 9): The Peppermint Twist

This puzzle is part of the Puzzling Stack Exchange Advent Calendar 2023. The accepted answer to this question will be awarded a bounty worth 50 reputation.< Previous Door Next Door > This puzzle ...
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### First digit of a large number

Can you find the first digit of $2^{2^{2^{2^{2^2}}}}$? Basically, it is $2$ to the $2$ to the $65536$ power. You cannot use a computer, but are allowed to use a calculator. Good luck!
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### Ended up with 'empathise'

I started off with a one-letter English language word. For every step, I added one letter of my choice, and re-arranged the letters to make a new word. By the end, I had: EMPATHISE What was the word ...
• 512
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### Minimum function optimization puzzle #4: Using negative numbers?

Previous puzzle Take this puzzle of mine that I created around a week ago: Take these 3 functions: $f(x):=x+8,g(x):=x^2-3,h(x):=\sqrt x$ Starting from $x=0$,\color{black}{\text{How many times will ...
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### Minimum function optimization puzzle #3: 3 functions

Previous puzzle Take this puzzle of mine I created recently: Let $f(x)=x+1$, $g(x)=x^2-1$, $h(x)=2x-4$. Starting with $x=0$ and applying these functions as needed, what is the minimum amount of times ...
• 2,413
1 vote
156 views

### A Hidato, but with no given numbers?

I can be a bit evil sometimes. Today, I am going to give you a Hidato with no numbers! It gets worse: This puzzle is on a Mobius Strip Y[1] However, I will give hints as to what the numbers are, so ...
• 2,413
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### Minimum function optimization puzzle #2

Previous puzzle Take this puzzle of mine I created about an hour ago Take two functions, $f(x):=x^2$ and $g(x):=x-3$. Starting from $x=0$ and applying these functions as needed, what is the minimum ...
• 2,413
1 vote
Here's a puzzle of mine that I created around 2 hours ago: Let $f(x):=x^2$ and $g(x):=x-4$. Starting with x=0, what is the least amount of times you need to apply the functions $f$ and $g$ so that at ...