If k is a confident integer and also k+1 objects are inserted into k boxes, climate at least one box consists of two or much more objects.

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Contradiction -Suppose no one of the k boxes has an ext than one object, then the total number of objects is k.Contradicts k+1 objects.

Example: There room 10 black color socks and also 10 white socks in a drawer. How numerous socks you need to pick (without looking) if you desire to undertake a pair that socks that the very same color?

The floor role assigns to a actual number the biggest integer that is much less than or same to x. Together x ⅃ ex:L 1/2 ⅃ = 0L -1/2 ⅃ = -1L 3.1 ⅃ = 3L 7 ⅃ = 7

The ceiling function assigns to a actual number the smallest integer the is better than or same to x. ⌈ x ⌉ex: ⌈ 1/2 ⌉ = 1⌈ -1/2 ⌉ = 0⌈ 3.1 ⌉ = 4⌈7⌉ = 7

If N objects are inserted into k boxes, then there is at the very least one box containing atleast ⌈ N/k ⌉ objects.Example: among 100 people, there room at the very least how many born in the exact same month? ⌈ 100/12 ⌉ = 9

How numerous cards need to be selected native a standard deck the 52 cards come guarantee the at least three cards the the very same suit room chosen?Assume 4 box (suits), ⌈ N/4 ⌉ >= 3N = 4(3-1) + 1 = 9

How countless cards indigenous a deck that 52 must be selected come guarantee that at the very least three hearts space selected?52 card = 13 mind + 39 not hearts.39 + 3 = 42

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Discrete math with Graph theory with Discrete math Workbook: interactive Exercises3rd EditionEdgar G. Goodaire

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