Problem of the Week
Problem C
Fractions to the Max
In diagram 1 below, four-fifths of a circle is shaded dark grey. In diagram 2,
one-sixth of a circle is shaded dark grey. In diagram 3, three-halves of a circle is
shaded dark grey.
Diagram 1
Diagram 2
Diagram 3
The three fractions illustrated have been formed using the positive integers 1, 2,
3, 4, 5 and 6 exactly once. When the three fractions are added together, the sum
is
4 1 3 24
5
45 74 37
7
+ + =
+
+
=
=
=2
5 6 2 30 30 30 30 15
15
Suppose that six different numbers are selected from the set
{1, 2, 3, 4, 5, 6, 7}. These six numbers are then used to form three fractions.
Each of the three numerators and three denominators must contain a different
digit from the selection. The three fractions are then added together.
Determine the largest possible sum that can be obtained.
Strands
Data Management and Probability, Number Sense and Numeration