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I disguised some words by shifting each of the letters the same number of steps through the alphabet, but then I forgot the number. Can you find it and restore the original words? vjsygfkusdwksjwi...
The area of a triangle can be calculated as half of the length of its base multiplied by its perpendicular height. This means that two triangles with the same length base and the same perpendicular...
Puzzle How short can you make a closed knight’s sightseeing tour? Terminology Standard terminology A chess board is an 8 by 8 chequerboard. A knight is a chess piece that moves 2 squares hor...
What does the following image represent? Description of above image for those who can’t view it: On the left: Horizontal line with a green happy face above it and a green letter K below it. ...
A large whiteboard has 2014 "+" signs and 2015 "−" signs written on it. You are allowed to delete two of the symbols and replace them according to the following two rules. If the two deleted symbo...
A blind person is handed a deck of 52 playing cards and told that exactly 10 of these cards are facing up. How can they divide the cards into two piles, not necessarily of equal size, with each...
There are $146$ marbles in a bucket. Delta and Epsilon play a game in which they take turns removing marbles from the bucket with Delta going first. At each turn the player can choose to remove e...
There are $100$ marbles in a bucket. Alpha and Beta play a game in which they take turns removing marbles from the bucket with Alpha going first. At each turn the player can choose to remove eith...
There are 8 binary strings of length 3. They are: 000 001 010 011 100 101 110 111 The goal of this puzzle is to arrange some 0’s and some 1’s around a circle (using as few 0’s and 1’s as ...
Given 2 bags and 5 stones, how would you place the stones into the bags so that the following three conditions are met: Both bags contain an odd number of stones. Every stone is inside a bag. ...
A 6x6 checkerboard is tiled arbitrarily with eighteen 1x2 dominoes. A new square is added to the right-hand side of the board, making the top row length 7. At any time you may move a domino from i...
Find the pattern in the fingers:
Draw a straight line through the center of the circle below to subdivide it into two halves so that each half will have the same number of occurrences of the letter A. Also each half will have the...
In each puzzle, fill the circles using all the positive integers 1, 2, 3, ... n, where n is the number of circles in such a way that consecutive numbers are NOT in circles that are joined with a li...
Join the pairs of dots marked similarly (i.e. A to A, B to B, etc.) using four lines which do not cross or touch at any point. The routes must follow the lines of the grid, and may not pass through...
Draw 3 lines, not necessarily straight, connecting the dots and satisfying all the following conditions: No line may touch or intersect another line. Every line must be completely inside the ci...
Eight different dominoes lie on a plane. No boundaries between the dominoes are shown in the figure. Draw these boundaries. Clarifications: A domino is made up two square halves joined at a com...
In the image below, nine toothpicks have been arranged to form the number 100. Can you move two toothpicks to form the word CAT. Attribution: Martin Gardner
In the diagram below, the number five is made up of 5 identical line segments. Reposition the line segments so the number five appears 5 times. You are not allowed to do anything except moving th...
Place an X into seven of the squares so that no square marked with an X is halfway between two other squares that are also marked with an X.
Imagine you are on a planet the same size as Earth but this planet is perfectly spherical and solid everywhere. Furthermore assume it has a North and a South Pole just like Earth and has direction...
Consider the following L-shaped 3-dimensional object made up of three unit cubes joined at their faces: Puzzle 1. Use 9 of the above L-shaped pieces to make a cube. Puzzle 2. Use 10 of the ...
Consider the following L-shaped 3-dimensional object consisting of 3 unit cubes joined at their faces: Is it possible to use six of the above L-shaped pieces to form the following 3-dimensiona...
Warmup puzzle: Here is an astronomical study for the little folks, although it may puzzle the grown ups as well. See how long it will take you to discover a perfect star in the above general mix...
Here’s a cute puzzle you can share with children. Can you find the intruder?
An Amazon is a fairy chess piece that can move like a queen or a knight. What is the maximum number of Amazons that can be placed on a 5x5 chessboard so that no piece attacks another? Attribu...
Three perfectly logical women, one of them blind, walk into a completely dark room full of hats. They all know that two of the hats are red and the rest are black. Each woman randomly selects...
Place a tile on each face of a regular dodecahedron so that the arcs on the tiles form a single closed loop. You may rotate the tiles provided they align with the pentagonal faces of the dodecahed...
Place a tile on each face of a regular octahedron so that the arcs on the tiles form a single closed loop. You may rotate the tiles provided they align with the triangular faces of the octahedron....
Place a tile on each face of a regular dodecahedron so that the arcs on the tiles form a single closed loop. You may rotate the tiles provided they align with the pentagonal faces of the dodecahed...
Place a tile on each face of a regular tetrahedron so that the arcs on the tiles form a single closed loop. You may rotate the tiles provided they align with the triangular faces of the tetrahedro...
Place a tile on each face of a regular icosahedron so that the arcs on the tiles form a single closed loop. You may rotate the tiles provided they align with the triangular faces of the icosahedro...
Consider the following L-shaped piece made of three unit squares joined at their edges: Allowing rotations of the L-shaped pieces, you can easily tile a 2x3 rectangle with two of the above L-sha...
Place 4 tiles on each face of a cube so that the arcs on all 24 tiles form a single closed loop. If you want to try a simpler version first, there is Closed loop on a side length 1 cube. You may ...
This post describes a classic puzzle. If you have previously seen this puzzle I request that you allow someone else to solve it and post their answer. Thank you! Mutilated chessboard problem: ...
In the diagram below, there are two types of L-shaped pieces (one made of 5 unit squares and the other made of 7 unit squares). The goal is to tile a 6x9 rectangle with one or more of the smaller ...
Place 9 tiles on each face of a cube so that the arcs on all 54 tiles form a single closed loop. If you want to try a simpler version first, there is Closed loop on a side length 2 cube. You may ...
Place a tile on each face of a cube so that the arcs on the tiles form a single closed loop. You may rotate each tile by any multiple of 90 degrees. The tiles to be used are equal numbers of 2 ki...
Grid This puzzle is played on a 5 by 5 grid of squares: Tiles There are 25 tiles to be placed on the grid, one on each square. They can each be rotated by any multiple of 90 degrees. Note ...
In this puzzle you arrange the numbers 1 through 9 into a $3 \times 3$ grid using each number exactly once. For example: 2 8 4 3 1 5 7 9 6 For each corner of the grid there is a corner sum w...
In the 4x4 grid below, fill each empty square with a number such that the numbers in each row form an arithmetic progression when read from left to right. Similarly, the numbers in each column shou...
In a bag are 26 bills. If you take out 20 bills from the bag at random, you are guaranteed to have at least one 1-dollar bill, two 2-dollar bills, and five 5-dollar bills. How much money was in t...
Using the numbers $3, \ 7, \ 25, \ 50, \ 75, \ 100$ (each used at most once), along with any number of the four basic arithmetic operations (addition, subtraction, multiplication and division) and ...
There are 6 permutations of the numbers 1, 2, 3. They are: 123 132 213 231 312 321 The goal is to make a string (as short as possible) using the digits 1, 2 and 3 so that each of the abov...
In the diagram below we have pentagon ABCDE with 5 edges and 5 diagonals. These 10 line segments are currently all colored black. The diagram contains several triangles but for this puzzle we are...
We had a sidewalk and driveway replaced this summer (standard concrete sidewalk, nothing fancy). We've been told not to use salt for at least the first winter because it will damage the young conc...
A 3 by 3 grid contains each digit exactly once, except one missing digit. A 3 by 3 arrangement of 9 such grids has one missing digit per grid. Each digit is missing from exactly one grid, except o...
Each instance of the word "banana" is in a straight line in one of the 8 directions displayed below: a . . . . . . . a . . . . . . . . a . n . . . . . . n . . . . . . . n . . . a . . . ...
Sometimes after I solve a Wordle puzzle I'll see what their bot had to say about my solution. Occasionally one of my words is a legitimate five-letter word (accepted by Wordle) but the bot says so...
Find three different integers A, B and C such that A+B, A+C and B+C are all powers of 2. Clarifications: A, B and C can be negative, zero or positive. Powers of 2 are: 1, 2, 4, 8, 16, ...
