Mathématiques

Question

Un nombre de 6 chiffres commence à gauche par le chiffre 1. Si on transporte le 1 à droite, le nouveau nombre ainsi obtenue est le triple du premier. Quel est le nombre initial?

1 Réponse

  • Bonsoir,
    142857 est la seule solution.

    DIM a AS INTEGER, b AS INTEGER, c AS INTEGER, d AS INTEGER, e AS INTEGER, f AS INTEGER
    DIM w1 AS STRING, w2 AS STRING
    DIM n1 AS LONG, n2 AS LONG
    w1 = SPACE$(6)

    MID$(w1, 1, 1) = "1"
    FOR b = 0 TO 9
        MID$(w1, 2, 1) = CHR$(48 + b)
        FOR c = 0 TO 9
            MID$(w1, 3, 1) = CHR$(48 + c)
            FOR d = 0 TO 9
                MID$(w1, 4, 1) = CHR$(48 + d)
                FOR e = 0 TO 9
                    MID$(w1, 5, 1) = CHR$(48 + e)
                    FOR f = 0 TO 9
                        MID$(w1, 6, 1) = CHR$(48 + f)
                        n1 = VAL(w1)
                        w2 = MID$(w1, 2, 5) + MID$(w1, 1, 1)
                        n2 = VAL(w2)
                        IF n2 = 3 * n1 THEN
                            PRINT w1, w2
                        END IF
                    NEXT f
                NEXT e
            NEXT d
        NEXT c
    NEXT b

    END


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