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.

See The Solution Submitted by K Sengupta

Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)

computer check of all a from 1 to a million (spoiler)

| Comment 1 of 4

For a = 1 To 1000000

d = a + 50

For c = a + 2 To a + 48 Step 2

b = (a + c) / 2

rmssq = (b * b + d * d) / 2

If rmssq = c * c Then

Text1.Text = Text1.Text & a & Str(b) & Str(c) & Str(d) & crlf

DoEvents

End If

Next c

Next a

finds only

29 47 65 79 as the values of a, b, c and d respectively.

Posted by Charlie on 2014-11-04 20:32:00

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