### 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?

### It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

### Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

# Sets of Numbers

##### Stage: 2 Challenge Level:

Children from Beaumaris North Primary School, Melbourne told us:

In our Year 3 Enrichment group we discussed all the possible sets that could be found. Here is what we found!
even numbers {$2, 8, 36, 56, 64, 136$}
odd numbers {$3, 13, 17, 27, 39, 49, 51, 91, 119, 121, 125, 143$}
multiples of one {all of them!}
multiples of $2$ {$2, 8, 36, 56, 64, 136$ - the same as even numbers!!}
multiples of $3$ {$3, 27, 36, 39, 51$}
multiples of $4$ {$8, 36, 56, 64, 136$}
multiples of $7$ {$49, 56, 91, 119$}
multiples of $8$ {$8, 56, 64, 136$}
numbers starting with $1$ {$13, 17, 119, 121, 125, 136, 143$}
square numbers {$36, 49, 64, 121$}
numbers containing $2$ {$2, 27, 121, 125$}
square roots {all of them are square roots !}
numbers containing $1$ {$13, 17, 51, 91, 119, 121, 125, 136, 143$}
numbers containing $6$ {$36, 56, 64, 136$}
cube numbers {$8, 27, 64, 125$}
numbers containing $3$ {$3, 13, 36, 39, 136, 143$}
prime numbers {$2, 3, 13, 17$}
numbers containing $9$ {$39, 49, 91, 119$}
numbers that you can subtract one from {all of them again!}
numbers between one and one hundred and forty four {all of them AGAIN!}
numbers between one and one hundred {$2, 8, 13, 17, 27, 36, 39, 49, 51, 56, 64, 91$}
whole numbers {all of them}
triple digit numbers {$119, 121, 125, 136, 143$}
numbers with double digits {$13, 17, 27, 36, 39, 49, 51, 56, 64, 91$}

We enjoyed this because we liked picking out different possibilities and seeing if they worked out. We could have submitted more but the bell rang! Thanks for the great challenge.

Olly from North Molton Primary also found:

multiples of $13$: {$13, 39, 91, 143$}
multiples of $17$: {$17, 51, 119, 136$}

... and multiples of $1$ which of course is all of the numbers.

Jin and Anushkawho go to Dubai International Academy had one more set:

digits add to $8${$8,17,125,143$}

Can you find any more? How about triangle numbers and tetrahedral numbers?