perplexus.info :: Just Math : Getting Floored With 28

Getting Floored With 28 (Posted on 2008-09-06)

The greatest integer ≤ Y is denoted by [Y] , and {Y} = Y - [Y].

How many distinct real Y satisfy this equation, whenever 1 ≤ Y ≤ 28 ?

{Y²} = {Y}²

Note: While a solution may be trivial with the aid of a computer program, show how to derive it without one.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The required number of distinct real Y satisfy the given equation is 757.

For an explanation, refer to the solution submitted by Paul in this location.

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In a similar manner, it can be established that the total number of distinct real Y satisfying the given equation for 1 ≤ Y ≤ N, whenever N is a positive integer, is equal to N² - N + 1.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Similar but not identical solution	K Sengupta	2008-09-17 12:57:33
re: solution	Charlie	2008-09-07 02:18:55
Similar but not identical solution	Paul	2008-09-06 22:31:54
solution	Charlie	2008-09-06 15:22:22

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