c) abcd - b53 = 2000+7000=9000
abcd-
b53
———-
9000
d-3=0 => d=3
c-5=0 => c=5
b = (1,2,3,4,5,6,7,8,9)
a = 9
abcd=(9153, 9253, 9353, 9453, 9553, 9653, 9753, 9853, 9953)
9 numere
d) a-b-c=7
abc=700, 801, 810, 902, 911, 920
e) abc - cba = 594
a≠0,c≠0
(100a+10b+c)-(100c+10b+a)=594 99a-99c=594
99(a-c)=594
a-c=594:99
a-c=6⇒a∈{7,8,9} c∈{1,2,3} b∈{1,2,3}
abc-cba=594
701-107=594 ; 711-117=594, ... ⇒ 10 numere de forma abc-cba=594 802-208=594,812-218=594, ... ⇒10 numere de forma abc-cba=594 903-309=594,913-319=594, ...⇒10 numere de forma abc-cba=594
In total sunt 30 de numere de forma abc-cba=594.
