Download Problem 26 - West Point

Problem of the Week
Week # 26
The republic of Algebraica lies so far behind the Iron Curtain that very few of us have
heard of it. This republic, anxious to flout “capitalistic conventions and superstitions,”
has introduced a scale of notation containing three extra digits – X, Y, and Z – which
are interpolated, very confusingly, in the ordinary denary scale. Thus we have:
Our numbers . . .
Their numbers . . .
1 2 3 4 5 6 7 8 9 10 11 12 13
1 2 3 X 4 5 Y 6 7 8 Z 9 10
Our 20 is represented by 1Y; our 100 by 77; and so on.
What (in the notation of Algebraica) is the square of their number 1X?