Mathematics

Mathematics, 02.10.2019 16:20, harleyandpope90

What is the number of rectangles on 10x15 checkerboard?

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Mathematics, 21.06.2019 22:00, Jasten

Set $r$ is a set of rectangles such that (1) only the grid points shown here are used as vertices, (2) all sides are vertical or horizontal and (3) no two rectangles in the set are congruent. if $r$ contains the maximum possible number of rectangles given these conditions, what fraction of the rectangles in set $r$ are squares? express your answer as a common fraction.

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Mathematics, 23.06.2019 17:30, LittleNerd2852

Suppose you have a 10 ă— 10 checkerboard and a deck of 2 ă— 2 cards with squares that match the size of the squares of the checkerboard, so 25 of these cards can be used to completely cover the checkerboard. if we allow the cards to overlap each other, there are many ways to cover the checkerboard. we say that an arrangement of cards is a covering if all of the cards in the arrangement are lined up with the squares on the checkerboard, and they are completely on the checkerboard, possibly overlapping, and every square of the checkerboard has at least one card on top of it. we call a covering of the checkerboard redundant if one of the cards can be removed and the checkerboard is still covered. a covering of the checkerboard is non-redundant if it is no longer a covering if any card is removed. clearly, the smallest non-redundant covering has 25 cards. the aim of this problem is to find bounds on the number of cards in the largest possible non-redundant covering. a) show that there is a non-redundant covering with 35 cards. b) show that every covering with 55 cards is redundant. c) can you improve these bounds?

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Mathematics, 02.07.2019 19:00, prishapup27

Five rectangles are arranged from the least to the greatest area and named a, b, c, d, and e in order of increasing area. all dimensions are whole numbers, and no 2 rectangles have the same area. determine the dimensions of all 5 rectangles using the following clues: the median area is 15 square units.rectangles b and d are squares.rectangles c and d have the same perimeter.rectangles a, b, and c have the same length.rectangles d and e have the same length.rectangles c and e have the same width.

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Mathematics, 30.10.2019 02:31, snikergrace

A) fund a recurrence relation for the number of ways to completely cover a 2 x n checkerboard with 1 x 2 dominoes. [hintconsider separately the coverings where the position in the top right corner of the checkerboard is covered by a dominopositioned horizontally and where it is covered by a domino positioned vertically]b) what are the initial conditions for the recurrence relation in part (a)? c)how many ways are there to completely cover a 2 x 17 checkerboard with 1 x 2 dominoes?

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