1st Key
The sum of two opposite faces of a dice always add up to 7. So choose any three numbers which would appear on a dice, which add up to 8. For each of these find the opposite number on the dice. Add these three to give 13
eg. if you chose 3+1+4 the opposite numbers are 4+6+3 = 13
2nd Key
The cards are 8, 5, 4, 7, 9. The last card a 9.
3rd Key
The diameter of each cirle is 5cm. The distance from the centre of each circle to the outer edge is the radius ir 2.5cm. So the distance between the centres is 9 - 2.5 -2.5 = 4
Now find 4 squared - 1 = 15
4th Key
By trial and error the correct numbers are:
7 2 6
5 1
3 4 8
Add the corner numbers (7+6+3+8)-10=14
5th key
Both trays hold 14 tarts. The first tray is full, but the second tray is only partly filled, so there are between 15 and 27 tarts.
The only number fulfilling the conditions in this range is 19.
Last question
Decoding the 5 keys gives the letters making the name SIMON, when rearranged.