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Testy Triplet Treat (Posted on 2013-08-04) Difficulty: 3 of 5
P(N) denotes the product of the digits in the base ten representation of N.

Determine all possible triplets (A,B,C) of positive integers with A ≤ B ≤ C that satisfy this system of equations:

A = P(B)+ P(C), B = P(A) + P(C), and C = P(A) + P(B)

Prove that there are no others.

No Solution Yet Submitted by K Sengupta    
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Some Thoughts results so far, but no proof in sight | Comment 1 of 7

So far the following (a,b,c) work: (5,5,10),(36,36,36) and (498,498,576).

The program has checked up to a+b=167903, last time I pressed a key to get a progress report.

DECLARE FUNCTION p# (x#)
DEFDBL A-Z
FOR tot = 2 TO 999999
    FOR a = 1 TO tot / 2
        IF INKEY$ > "" THEN PRINT tot, a
        pa = p(a)
        b = tot - a
        IF b >= pa THEN
            pb = p(b):
            c = pa + pb
            IF c >= b THEN
                pc = p(c)
                IF a = pb + pc AND b = pa + pc THEN
                    PRINT a, b, c
                END IF
            END IF
        END IF
    NEXT a
NEXT tot

FUNCTION p (x)
prod = 1
n = x
WHILE n > 0
    prod = prod * (n MOD 10)
    n = n \ 10
WEND
p = prod
END FUNCTION

 


  Posted by Charlie on 2013-08-04 12:53:46
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