You may also like

Network Trees

Explore some of the different types of network, and prove a result about network trees.

Always Two

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Symmetricality

Five equations and five unknowns. Is there an easy way to find the unknown values?

Continuing to Explore Four Consecutive Numbers

Age 14 to 16
Challenge Level


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


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

  1. Why can't $bd-ac$ be even?
     
  2. What is $bc-ad$ always equal to?
     
  3. Why must the sum $a+b+c+d$ have an odd factor?
     
  4. Why can't the sum $a+b+c+d$ be a multiple of $4$?
     
  5. 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.