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Find a rectangular grid of the smallest area that satisfies the following:
Each cell contains an integer between 1 and 4 inclusive.
The grid follows the Fillomino rule:
When the cells are divided into connected groups containing same numbers, each number belongs to a group of that many cells.
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1
The man wishes to remove this string loop from his right hand without cutting the string. His right hand is inside his pocket and he isn't allowed to take out this hand from the pocket. He can only use his left hand.
How can he do this?
I have seen the solution but couldn't understand it.
From: ...
0
My roommate asked me to buy some stuff from the grocery store.
“What am I supposed to get from the grocery store, sir?” I replied.
“Man, get out and just buy the dang groceries, WILL YOU!?!” shouted my roommate.
What am I supposed to buy?
Hint:
Inspired by Fitting the 9th piece into the pizza box
2 pizzas with radius r are each cut into 8 identical slices. 6 pieces were eaten so there are 10 pieces left. They need to be put in a square box without cutting or overlapping pieces. What is the minimal side length of the box, expressed in r?
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Seven different digits are placed in a row. The products of the first 3, middle 3 and last 3 are all equal. What is the middle digit ?
Source: unknown
This is a cryptic crossword. All clues given are across clues, to be initially entered as numbered in the grid. Coloured squares in the grid provide the down-element: each of five colours indicates that the letter that would go in that cell must be duplicated a prime number of rows below it (co...0
On an infinite complete binary tree, each edge is independently labelled $H$ or $T$ by flipping an unbiased coin.
Let $X=$ the length of the longest path of consecutive $H$s starting from the root.
Here is an example with $X=3$.
What is the expectation of $X$?
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Cryptic crosswords often use abbreviations to clue individual letters or short fragments of the overall solution. These include:
Any conventional abbreviations found in a standard dictionary, such as:
"current": AC (for "alternating current"); less commonly, DC (for "direct current"); or even I (the symbol used in physics and electronics)
Roman numerals: for example the word "six" in the clue might be used to indicate the letters VI
The name of a chemical element may be used to signify its symbol; e.g., W for tungsten
The days of the week; e.g., TH for Thursday
Country codes; e.g., "Switzerland...
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