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National and Regional Contests
Chile Contests
Chile National Olympiad
1989 Chile National Olympiad
1
1
Part of
1989 Chile National Olympiad
Problems
(1)
1998 has same sum of digits in base b and 10 (Chile NMO 1989 P1)
Source:
11/19/2021
Writing
1989
1989
1989
in base
b
b
b
, we obtain a three-digit number:
x
y
z
xyz
x
yz
. It is known that the sum of the digits is the same in base
10
10
10
and in base
b
b
b
, that is,
1
+
9
+
8
+
9
=
x
+
y
+
z
1 + 9 + 8 + 9 = x + y + z
1
+
9
+
8
+
9
=
x
+
y
+
z
. Determine
x
,
y
,
z
,
b
.
x,y,z,b.
x
,
y
,
z
,
b
.
number theory
sum of digits
Digits