Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some other possibilities for yourself!

Have You Got It?

Can you explain the strategy for winning this game with any target?

Factors and Multiples Puzzle

Stage: 3 Challenge Level:

We received many correct solutions to this puzzle:

Elizabeth, Holly, Kelly, Harrison, Harry and Matthew from Miss Rowcliffe's Maths Class in Upton Heath C of E Primary School in Chester sent us this solution:

 Numbers less than 20 5 18 15 11 1 Numbers more than 20 30 36 45 23 25 Odd numbers 35 21 55 7 9 Even numbers 20 24 10 2 16 Factors of 60 60 12 6 3 4 Multiples of 5 Multiples of 3 Triangular numbers Prime numbers Square numbers

Lydia from Woolmer Hill School sent in this solution:

I found out that the numbers less than $20$ and the numbers more than $20$ are on the same side and also the odd numbers and the even numbers are on the same side.

 Numbers lesss than 20 16 1 18 15 7 Numbers more than 20 25 30 60 35 23 Odd numbers 9 5 45 55 11 Even numbers 4 12 24 20 2 Triangular numbers 36 6 21 10 3 Square numbers Factors of 60 Multiples of 3 Multiples of 5 Prime numbers

Vicky and Katrina, also from Woolmer Hill School, submitted this solution:

 Numbers lesss than 20 4 18 6 10 11 Triangular numbers 1 21 15 45 3 Odd numbers 25 9 5 55 7 Even numbers 16 12 30 20 2 Numbers more 20 36 24 60 35 23 Square numbers Multiples of 3 Factors of 60 Multiples of 5 Prime numbers

Ben, Henry, Joseph, Simon, Michael and Jake from Hampton School sent us these three different solutions.

Heidi, Lucy and Natasha from Millais School sent us this record of their work:

Initially we looked at the headings and found those that could not have any overlap,
e.g. Odd and evens, primes and square numbers, numbers under and over 20.
We placed those headings first and then put the others in place.
Here is their completed board.

Poppy and Hazel, also from Millais School, reported that:

We started by trial and error and got rather frustrated!
We realised that some of the headings had to be paired up because number could not appear in both categories, e.g. odds and evens, primes and squares.
From there we placed the headings in the table and gradually moved the others around until it worked. Interestingly, our solution was different to others in our class.

Lara and Jeni, again from Millais School, sent us a different solution

Congratulations also to Sam from Ridgewood School, Amy from SMTS and Polly and Heather from Hertfordshire and Essex High School who all sent us correct solutions. Well done to you all.