Weekly Problem 16 - 2012
If the odd numbers on two dice are made negative, which of the totals cannot be achieved?
Consecutive Negative Numbers
Stage: 3 Challenge Level:
Do you notice anything about the solutions when you add and/or
subtract consecutive positive numbers?
You could start by considering four consecutive positive numbers before moving on to
consider four consecutive negative numbers.
If you have looked at several sets of consecutive numbers and
noticed some similarities in the solutions, you may be wanting to
explain why they occur. An algebraic representation of the
situation might help you with this:
if $a$ is your smallest number, the four consecutive numbers are
$a$, $a+1$, $a+2$, $a+3$
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.