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National and Regional Contests
Canada Contests
Canada National Olympiad
1987 Canada National Olympiad
2
All ways of representing 1987 in another base [Canada 1987]
All ways of representing 1987 in another base [Canada 1987]
Source:
September 30, 2011
Problem Statement
The number 1987 can be written as a three digit number
x
y
z
xyz
x
yz
in some base
b
b
b
. If
x
+
y
+
z
=
1
+
9
+
8
+
7
x + y + z = 1 + 9 + 8 + 7
x
+
y
+
z
=
1
+
9
+
8
+
7
, determine all possible values of
x
x
x
,
y
y
y
,
z
z
z
,
b
b
b
.
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