perplexus.info :: Just Math : Floor Function Query

Floor Function Query (Posted on 2016-01-25)

F(x) is a real valued function such that:
F(x) = floor(x) +floor(10x)+floor(100x)+floor(1000x)
Determine all possible values of a positive integer N < 2016 such that:
F(x) = N has no solution for x, but:
Each of the equations: F(y) = N+11 and F(z) = N+111 has at least one solution in y and z.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

The complete list of possible values for N is 1108 + 1111*k for all non-negative integers k.
For an explanation, refer to the solution submitted by Charlie in this location.

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

	Subject	Author	Date
	computer solution	Charlie	2016-01-25 11:16:57

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