Many Bricks

Number Theory Level 3

Each brick is assigned a number which is the sum of the numbers on the two bricks below it. Only some of the numbers are showing.

Is the number on the top brick odd or even?

Odd Even Not enough information

1 solution

Marta Reece
May 14, 2018

The number of the leftmost brick in the bottom row is $3$ .

The bottom row is then $3, 2, a_1, a_2, a_3, a_4, a_5, a_6, 2$ .

The number on the top brick can be obtained from the appropriate row of Pascal's triangle and it is:

$3+8\cdot 2+28\cdot a_1+56\cdot a_2+70\cdot a_3+56\cdot a_4+28\cdot a_5+8\cdot a_6+2$

All of the terms are even except the first, $3$ , so the number is $\boxed{\text {odd}}$ .