Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Label this plum tree graph to make it totally magic!
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
In March we posed the problem: "The number $3723$ (in base $10$) is written as $123$ in another base. What is that base?" ............ The answer to this can be found in the March problem archive.
We could have written this question as:
Find b where $3723_{10} = 123_{b}$ So, moving on ................... $123_{20}$ is $1 \times 20^2 + 2 \times 20 + 3 = 443_{10}$ $123_{21}$ is $1 \times 21^2 + 2 \times 21 + 3 = 486_{10}$ $123_{22}$ is $1 \times 22^2 + 2 \times 22 + 3 = 531_{10}$ $531 - 486 = 45$
$486 - 443 = 43$
Investigate these differences when $123_{b}$ is converted to base $10$ (for different values of $b$).