Challenge Level

*This problem follows on from, Starting to Explore Four Consecutive Numbers.*

**Take four consecutive numbers, $a$, $b$, $c$, $d$.**

- Why can't $bd-ac$ be even?

- What is $bc-ad$ always equal to?

- Why must the sum $a+b+c+d$ have an odd factor?

- Why can't the sum $a+b+c+d$ be a multiple of $4$?

- Which consecutive numbers are such that $a+b+c+d$ divides exactly by $3$?

*If you enjoyed working on this problem, you may now want to take a look at the follow-up problem, Is There More to Discover About Four Consecutive Numbers?. *

*With thanks to Don Steward, whose ideas formed the basis of this problem.*