Sum of Dot Products

Probability Level 2

Let a1,,a16a_1, \ldots, a_{16} be the list of 24=162^4 = 16 distinct vectors which have 4 coordinates, whose values are either 0 or 1. What is the maximum possible value of a1a2+a3a4++a15a16a_1 \cdot a_2 + a_3 \cdot a_4 + \cdots + a_{15} \cdot a_{16}?

Details and assumptions

uv u \cdot v represents the dot product of vectors.

Examples of vectors which have 4 coordinates and whose entries are either 0 or 1 are: (0,0,0,0),(1,1,1,1),(0,1,0,1),(1,0,0,0) (0, 0, 0, 0), (1, 1, 1, 1), (0, 1, 0, 1), (1, 0, 0, 0) .

The list is a set of all the 16 distinct vectors which satisfy the condition.

×

Problem Loading...

Note Loading...

Set Loading...