老人分马

Author: 广东贾玉宝 Date: 1994-01-28

        因为1/a+1/b+1/c=n/(n+1)<1所以a>=2，b>=3，c>=7，则n/(n+1)=1/a+1/b+1/c<=1/2+1/3+1/7=41/42，即n/(n+1)<=41/42，解得n<=41.如此有如下程序：
        5 REM '分马'
        10 PRINT "N", "X", "Y", "Z"
        20 FOR N = 6 TO 41
        30 FOR X = 3 TO (N + 1) / 2
        40 FOR Y = 2 TO X - 1
        50 Z = N - X - Y: IF Z >= Y THEN 100
        60 IF INT((N + 1) / X) <> (N + 1) / X THEN 100
        70 IF INT((N + 1) / Y) <> (N + 1) / Y THEN 100
        80 IF INT((N + 1) / Z) <> (N + 1) / Z THEN 100
        90 PRINT N, X, Y, Z
        100 NEXT Y, X, N
        110 END
        PRINT
        以上程序用Basic语言编写，在PC-286(无硬盘)机上，调试通过。