Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.
We had quite a few responses from pupils who
had found out things by exploring this situation. Calum,
Christopher and Matthew from St. Andrews in Scotland wrote to
Sayeed from St. Michael's London also
sent in a well thought out reponse:-
This is my answer when starting with $4$ digits:
$3243, 122314, 21221314, 31321314,
It will continue as the same number forever.
I notice: Each row has two more digits then the previous row
until the rows have the maximum amount of digits ($8$) possible. In
each row with the maximum digits, the second digit always has a
$1$, the fourth digit always has a $2$, and the sixth digit always
has a $3$ and so on. Every row ends in $14$ excluding the starting
row. This is my answer when starting with $5$ digits:
$22411, 212214, 213214, 21221314,
31321314, 31123314, 31123314$
I notice the same thing that happens with the starting $4$ digit
row except the rows getting two more digits each time until there
are maximum digits. I also notice that with the starting four digit
row it takes four counts till the number continues as the same
number forever. But for the starting five digit row it takes five
counts till the number continues as the same number forever!
Thomas from Colet Court School said the
following and attached his numbers.
Finally, Miss Stanley's Numeracy group from
Greystoke Leicester wrote:-
Well done to all the contributors,
it sounds as if you really enjoyed this. (A late arrival came from
Adam at Cypress School who noted something special about $1$ &
$4$. I am wondering if that was because it was not a usual
thing you'd find going on in many Mathematics lessons? On the last
day of the month we recieved this excellent presentation of Oscar