What is Ziffle?
There's a planet out in space called Zargon ........
On this planet these are numbers that are called ziffles
These numbers are ziffles $56, 105, 28, 63, 49$
These numbers are not ziffles: $100, 18, 65, 9, 76$
Only two of these numbers are ziffles: $16, 14, 57, 24, 70$
So what is special about the ziffles?
Lots of people sent in solutions for this one.
Becky from Wheelers Lane Junior School, Birmingham, England gave one of the best explanations ...
"I found this quite an easy puzzle because I know my times tables well. I soon spotted that 56, 28, 63 and 49 were all in the seven times table and later found out that 105 was. I also noticed that 100, 18, 65, 9 and 76 were not in the seven times table. I then worked out that 14 and 70 were".
As Susannah from Headington Junior School, Oxford says, "A ziffle is a multiple of 7".
Joshua from Ampthill, Bedfordshire, Emma from Cambridge and Matthew from Hethersett Old Hall Juniors also sent in correct solutions.
Why do this problem?
This short problem encourages children to look for patterns and apply knowledge of their times tables and of the properties of numbers.
Possible approach
Encourage the children to look at the sets of numbers in turn and explore their characteristics and properties.
Key questions
Are they all odd in one set and even in the other?Are they prime numbers?
Are they triangle numbers?
Are they all in the five times table?
How about other tables?
Possible extension
Either you or your pupils could make up their own problem using, for example, multiples of $13$ or another table that they might like to practice.
Possible support
Take an easier table and develop sets of multiples and non multiples to identify.Use concrete apparatus to explore divisibility such as Multilink cubes.