At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the assets of the players at the beginning of the evening?
According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
find them? What rectangular boxes, with integer sides, have their
surface areas equal to their volumes?
There were a few complete solutions sent in and many who showed us what the final result at the tables would be, i.e. $5$ at the $1$ table, $10$ at the $2$ table and $15$ at the $3$ table.
The full solution showing fractions at each stage were received from Adriel, Emily and Aswaath from the Garden International School in Maylasia. Also Daniel at Staplehurst School and Megan at Twyford School. Here is Emily's contribution.
Yinyi who goes to the Chinese International School, sent us this picture of the table he made to work on the solution:
Finally, thank you to Sam and Jack from Orchard Junior School who sent in a table of their solution for a class of 24 children. Sam and Jack chose to represent the fractions of chocolate as decimal numbers but unforunately, I think you made a little slip-up for the last four pupils in the class.
Well done all of you for your work on quite a difficult challenge.