perplexus.info :: Just Math : RMS Rigor

RMS Rigor (Posted on 2014-11-04)

A < B < C < D are four positive integers such that:

(i) B is the arithmetic mean of A and C and:
(ii) C is the rms of B and D, and:
(iii) D-A = 50

Determine all possible quadruplets satisfying the given conditions and prove that there are no others.

Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Solution: (Hide)

(A,B,C,D)= (29, 47, 65, 79) is the only possible solution that satisfy all the given conditions.
For an explanation, refer to the analytic solution submitted by Steve Herman in this location.
Steve Herman has also extended the provisions of the given problem in this location.

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

Subject	Author	Date
General solution ( D-A = K )	Steve Herman	2014-11-05 21:23:55
Analytical solution (without quadratic equation)	Steve Herman	2014-11-05 18:18:05
Almost full solution	Jer	2014-11-05 13:11:15
computer check of all a from 1 to a million (spoiler)	Charlie	2014-11-04 20:32:00

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