Sets and Groups - March 2005, Stage 3&4

Problems

problem icon

Consecutive Seven

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

problem icon

Shuffle Shriek

Stage: 3 Challenge Level: Challenge Level:1

Can you find all the 4-ball shuffles?

problem icon

Stars

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

problem icon

Arithmagons

Stage: 4 Challenge Level: Challenge Level:1

Can you find the values at the vertices when you know the values on the edges?

problem icon

Spot the Card

Stage: 4 Challenge Level: Challenge Level:1

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

problem icon

Sheffuls

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Discover a handy way to describe reorderings and solve our anagram in the process.

problem icon

Zodiac

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level: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.
Copyright © 1997 - 2018. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.