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An a × b rectangle can be packed with 1 × n strips if and only if n divides a or n divides b. [15] [16] de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]
The balls into bins (or balanced allocations) problem is a classic problem in probability theory that has many applications in computer science. The problem involves m balls and n boxes (or "bins"). Each time, a single ball is placed into one of the bins.
Michie completed his essay on MENACE in 1963, [4] "Experiments on the mechanization of game-learning", as well as his essay on the BOXES Algorithm, written with R. A. Chambers [6] and had built up an AI research unit in Hope Park Square, Edinburgh, Scotland.
A special case of bin packing is when there is a small number d of different item sizes. There can be many different items of each size. There can be many different items of each size. This case is also called high-multiplicity bin packing , and It admits more efficient algorithms than the general problem.
The illusion occurs when a person underestimates the weight of a larger object (e.g. a box) when compared to a smaller object of the same mass.The illusion also occurs when the objects are not lifted against gravity, but accelerated horizontally, so it should be called a size-mass illusion. [6]
The phenomenon is also known as the muesli effect since it is seen in packets of breakfast cereal containing particles of different sizes but similar density, such as muesli mix. Under experimental conditions, granular convection of variously sized particles has been observed forming convection cells similar to fluid motion. [5] [6]
In Ars Conjectandi (1713), Jacob Bernoulli considered the problem of determining, given a number of pebbles drawn from an urn, the proportions of different colored pebbles within the urn. This problem was known as the inverse probability problem, and was a topic of research in the eighteenth century, attracting the attention of Abraham de ...
Method of swirling an Erlenmeyer flask during titration. The slanted sides and narrow neck of this flask allow the contents of the flask to be mixed by swirling, without risk of spillage, making them suitable for titrations by placing it under the buret and adding solvent and the indicator in the Erlenmeyer flask. [7]