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?

Starting to Explore Four Consecutive Numbers

Age 11 to 16
Challenge Level


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

  1. (a) The four consecutive numbers sum to $130$. What are they?
    (b) The four consecutive numbers sum to $-38$. What are they?
     
  2. The sum of the first three consecutive numbers is $10$ more than the fourth. What are the four numbers?
     
  3. What is $(a+d)-(b+c)$? Why?
     
  4. Explore $a+b+c-d$.


If you enjoyed working on this problem, you may now want to take a look at the follow-up problem, Continuing to Explore Four Consecutive Numbers.


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