# Questions tagged [no-computers]

A puzzle designed to be solved without using calculators, online decoders or computer programming. You're still allowed to use a computer to post the solution; Stack Exchange doesn't support smoke signals yet.

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### Perfect power nim

Let $m,n$ be positive integers. Ann and Ben has $m$ stones, and each of them takes exactly the perfect power of $n$ stones ($n^k$, where $k$ is a nonnegative integer) in order, starting from Ann. Who ...
131 views

### Fill in numbers on the cube … again!

You are given a cube. You are told to fill in each face randomly with some of the numbers $4, 5, 6, ..., 11$, with no repetition. What is the probability that for each two faces that are connected by ...
3k views

### Today is a sad day

Today is a sad day - Today, it was supposed to be my big day to shine! But unfortunately that is no longer the case. I have heard from others here that puzzle-making is a great way to drown out one's ...
331 views

### Tempoverlustspiel

Tempoverlustspiel-A German word that roughly translates to "loss of tempo game." An interesting chess term that I leaned a while ago. With White to move in the below position, how many moves ...
164 views

### Fill in numbers on the cube!

You are given a cube. You are told to fill in each vertex with the numbers $4,5,6,...,11$, with no repetition. What is the probability that for each two vertices that are connected by a common edge, ...
862 views

### 4k reputation special: “I hate square numbers!”

There is a large prison, with exactly 4000 prisoners. The warden noticed that there were too many prisoners, so they lined up all the prisoners, and repeated the following procedure until less than ...
268 views

### Elementary word-search

Here's a simple wordsearch: ...and the text version: ...
1k views

I saw this interesting problem in a Mathematics book in Chinese(I translated it): You and your friend is playing a game. There is a square swimming pool, and you are in the middle of it. Your friend ...
363 views

### Mini 8 queens puzzle

On a 5x5 chessboard, place 5 black queens and 3 whites queens so that no queens are attacking those who are of different color. Furthermore, the numbers indicate how many queens are attacking the ...
251 views

### Square made up with polyominoes

A 3 x 6 rectangle has 2 holes in it as shown. Can you cut it into 3 polyominoes with different areas so that they can form a square? The pieces can’t be flipped when they form the square and two ...
517 views

### A Puzzling Cryptex

I was hanging out in the Puzzing.SE lounge (the beanbag chairs are heaven) when some random person walked up. They said, "I love this place! Would you try my puzzle?" Their puzzle was a cryptex (...
172 views

### Can you fill $3 \times 3$ magic square?

In the magic square Each number in the matrix is unique and natural. Each row, column and the two diagonals add up to the same number (the magic constant). Can you fill in the missing numbers? \...
624 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 ...
106 views

### Find the unique passcode

"Is this the Coldport Lost Property Office? I think I left my puzzle-book on the train this morning, and I was hoping someone had handed it in." The speaker was a tall gentleman with a six-...
441 views

### A Puzzle about “Codeforces Subsequences”

I'm quite intrigued by an "easy" problem in recent Codeforces contest: Codeforces Subsequences. In this problem, you have to create a string $T$ as shortest as possible such that $S =$ &...
272 views

### Fibonacci progression

In a number sequence, 1, 13, 169 and 2014 are respectively the first four terms of the sequence. The next terms are equal to the sum of the four numbers that precede them. For example, the fifth term ...
2k views

You met a genie. He gets $150$ magic lamps out, which are numbered from $1$ to $150$. You have to colour each lamp red or blue. After colouring, the genie will count the number of triples $T$ of magic ...
3k views

### Lottery strategy

In a city, the official lottery consists of scratch cards that cost 10 bucks each. Each scratch card contains 36 squares with a hidden number on each square : 21 of them are “zeroes”, 9 of them are “...
594 views

### In honour to 2004

222444 is the smallest number that is divisible by 2004 and only contains the digits 2 and 4. What’s the next number that has the same properties? Hint:The number is 11 digits long.
760 views

### Numbers that are the sum of the cubes of their digits

There are just four 3-digit numbers which are the sums of the cubes of their digits. For example: $370 = 3^3 + 7^3 + 0^3$ and $371 = 3^3 + 7^3 + 1^3$. Without using a calculator/computer, can you ...
76 views

### Multiples of their reversals

8712 and 9801 are the only 4-digit numbers which are multiples of their reversals: 8712 = 4*2178 and 9801 = 9*1089. Without using a calculator/computer, can you find two 5-digit numbers with this ...
283 views

### Simple Homeworlds puzzle

On this site, we have numerous chess puzzles. however, we do not seem to have any Homeworlds puzzles, the game of space kings (yes this can be tagged outer space thank you very much.) Hence, here is ...
453 views

I have one Math puzzle to which I think I found the solution but wanted to check your opinion on it. The puzzle is the following: George has 1 banknote of 100 (the currency does not matter. Lets name ...
684 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 ...
3k views

### A 16 Clue Sudoku Puzzle (but the kings can't be in check)

An entry in the 19th fortnightly challenge... Above is a 9x9 "chess" board with some pieces already laid out, your goal is to fill the board completely, following standard Sudoku rules (i.e. every ...
503 views

### Some luck involved

Can you guess the theme? OK, feel free to reverse image search, it's been many days now. Slight Tip: Tip 1: Tip 2: Last Tip:
576 views

### Multiplicative sudoku (don’t use computers please)

If I place all the numbers from 1 to 9 in a 3x3 grid and I add the products of each row and column, then what is the minimal and the maximal sum? For example, the sum is 450 on the picture above
298 views

### Functional Equation: Squeeze it

Determine whether there exists a function $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$f\big(x^3+x\big)\le x\le\big(f(x)\big)^3+f(x)$$ for all $x\in\mathbb{R}$. Source: Math Excalibur Volume 22 No....
275 views

### Add a divisor! A game

Let $k$ be a positive integer. Amy and Ben are playing a game, with the number $1$ written on the whiteboard initially. Amy and Ben do the following in order, starting with Amy: Suppose the number on ...
125 views

### Find a factor #1

The series of Find a factor puzzle is started by Culver Kwan, and asks the solver to identify a factor of a certain large number within a certain range using some mathematical identities. This should ...
1k views

### Some numbers are more equivalent than others

[Second part and bounty challenge appended in May 2020]           ALL ANIMALS ARE EQUAL    BUT ...
637 views