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Welcome to growadandelion.ca! In this post we will talk about our website features that will get you started whether you are a visitor browsing through the creations we host or a creator looking to share your own with us.
Welcome to growadandelion.ca! In this post we will talk about our website features that will get you started whether you are a visitor browsing through the creations we host or a creator looking to share your own with us.
The original problem asks for a combination of 1x2 and 1x3 rods that can tile a 5x5 square. Tiling problems have a tendency to get complicated quickly, so let’s start small.
We start with a polygon and a number of points inside it. We are asked to draw line segments between the points to subdivide the entire polygon into triangles.
The original problem asks to cut a square by drawing straight lines between any number of midpoints of sides and corners of the square such that a resulting region is 1/5 of the area of the whole square.
Imagine instead of a two dimensional grid, we are now filling a 3D grid made up of nxnxn unit cubes with numbers 1 to n such that every row, column, and depth has exactly one of each number.
This problem is inspired by this geometry puzzle on Twitter. The original problem asks to find the ratio between two equilateral triangles fitted into a square. Let’s generalize it.
Today let’s explore one of the deviations from the standard sudoku rules that every row, column, and subgrid (excluded so we can generalize to non-perfect-square side lengths) must have exactly one of each number from 1 to n, where n is the side length of the sudoku puzzle. Let’s include the new rule that a valid solution to a sudoku puzzle must also have one of each number in each of its two diagonals.
Now let’s consider the surfaces we obtain by stretching and gluing the sides of a square together.
Sudoku is a one-player game where the player tries to fill the spaces of an nxn grid using numbers 1 to n, where n is a natural number, such that every column and every row contains exactly one of each number.
Let’s define polycubes as three dimensional shapes made up of unit cubes connected by shared faces.
Let’s consider tiling square grids using polynominoes of any number of units.
If we separate all tetrominoes according to their perimeters, we would have two groups.
Polynominoes are figures made up of square units connected by edges.
Let’s consider tiling square grids with tetrominoes. Pieces can be rotated, reflected, and repeated as needed.
Consider drawing squares using the lattice points in a grid as vertices.
Consider trying to scramble a string of numbers, say 1, 2, 3, 4, 5, but with the requirement that none of the numbers can end up where they started. Let’s define this as a complete scramble.
We want to flatten the outer shell of a cube without tearing or stretching the surface.
For all questions in this problem, let’s ignore the effects of gravity, which means higher unit cubes can float in space without lower unit cubes to support them.
Let’s say instead of “bisecting” the triangle, we draw a line from the top vertex to the base with a length that is the average of the remaining two sides...
Let’s start with a right triangle with a height of 1 unit and consider two ways of dividing it into two triangles.
We choose one space in a rectangular grid made of unit squares, and we count the number of squares or rectangles that cover this space.
Let’s consider all real valued functions whose inverse is the function itself. Since the graphs of these functions are their own mirror images across the line y=x, let’s define these functions as mirror functions.
Continuing from last week’s problem about counting squares, let’s look at the related problem of counting the number of rectangles in a grid, with extensions
Consider the widely known problem of counting the number of squares in a square grid. Today we will try to extend the problem.
Consider this family of popular puzzles: You have two empty water jugs with no markings. One holds exactly 8 liters of water when full, and the other holds 3 liters. You also have a full tub with an endless supply of water and another large unmarked empty jug of unknown volume. The goal is to measure out a given volume of water to put into the large jug using the other two jugs.
Starting with a square, choose two points on the perimeter of the square to make a line, and then move both end points incrementally in the same direction (clockwise or counterclockwise) and the same distance along the perimeter of the square to make subsequent lines.
In a game of Peg Solitaire, 32 pegs are arranged in a cross shaped grid with the center peg removed. In each move, the player is allowed to move one peg over another, vertically or horizontally onto an empty space, and remove the peg that was jumped over. The game continues until no legal move is available, and the goal is to have as few pegs remaining as possible when the game ends. A perfect game would end with a single peg back in the center of the board.
Tower of Hanoi is a one-player game using three vertical rods and a number of disks, all of different diameters. The goal of the game is to move the entire pile of disks onto one of the other two pegs.
The standard number system we use today is called decimal numbers, or base 10, meaning at every digit, we count to 9 before carrying one to the next smallest digit.
A continued fraction is a way to represent any real number as a sequence of integers by writing down the integer part of the real number and taking the reciprocal of the remaining part at each iteration.
A perfect number is a natural number that is equal to the sum of all of its proper divisors (divisors that are less than the number itself). For example, 6 is the smallest perfect number because its proper divisors, 1, 2, and 3, add up to exactly 6.
Consider all pairs of natural numbers that add to 9, which pair has the largest possible Least Common Multiple?
Triangular numbers and trapezoidal numbers are both natural numbers that can be expressed as the sum of more than one consecutive natural numbers.
Sliding numbered blocks in a square grid to put them back in numerical order.
Lights connected in a string or a loop, each attached to a switch that will change the state of the light itself and its neighbours when pressed.
Connecting letters on the left to their matching letters on the right without crossing any lines.
The card game Seven is one where players take turn extending the numerical sequences of cards in their respective suits.
Irish Snap is a multiplayer card game using the standard deck of 52 playing cards where each player takes turns laying down one face up card each while counting. I.e. the first person says “ace” while laying down the first card; then the second person says “two” while laying down the next card. This process is repeated until the card that has just been laid down matches the number the person just called. When such a match happens, all players race to slap a hand on top of the pile of cards, and the slowest person has to take the pile into their hand. The first person to empty their hand wins.
Cutting three dimensional shapes and looking at the possible shapes of the cross section.
Cutting 3D shapes parallel to the base such that the top and bottom resulting portions have the same volume.
Is this method of constructing a regular polygon an approximation? or theoretically accurate?
Separating egg-laying chickens from non-egg-laying chickens by keeping them in boxes.
Counting the number of ways to make an exact amount using Canadian coins and bills.
“等等,你怎么又写我死掉的故事?”灰灰生气地说。 “啊,真的!一不留神就又选了这样的故事。”小丹不好意思地挠了挠脸。“不过别急,这个王子还是这个故事的主角呢。”
那是这个世界唯一的魔法,可以阻挡整个世界的寒冷。小轩隐约记得,里面有温暖的阳光,有带着花香的微风,有鸟叫声,有干净流动的泉水,还有人对他说: “安心住下吧,我会保护你的。”
从前有一座很高很陡峭的山,叫做飞龙山,山顶上有一个古老的飞龙巢穴。山脚下有个同样古老的村子,叫做翠石村,村民们以偷盗飞龙的宝石为生。村里有个习俗,每个刚满十三岁的孩子,不论男女,都要独自爬上山顶,拿到一颗宝石,然后安全回来。
孔融看着粉丝转述的父亲的回忆,细细品着字里行间透着的自豪。其实这并不像父亲所说的,是个关于分享和谦让的故事,而是一个关于与人相处和说话方式的故事,但这一点只有孔融自己知道。 就当是细节,忽略不计吧。(687字)
Welcome to growadandelion.ca! In this post we will talk about our website features that will get you started whether you are a visitor browsing through the creations we host or a creator looking to share your own with us.
A rough painting with crayons and pencil crayons on lined A4 paper, of full moon in a clear sky over still water.
A problem about sorting a shuffled set of cards back into the original order
A question about arrangement of coloured chips on a Connect Four board
Four problems about splitting a natural number into smaller natural numbers.