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Skippy's real name is SIMON
1) the dice problem gives you a key number of 13 as the combination is 6+6+1 .

2)The last card is number 9 and is the 2nd key number because the order is 8 5 4 7 9

3)In the third room the distance between the centre of the two circles is 4cm and the key number is 15 because 4x4 =16 -1 =15

4)the numbers on the corners are 3 8 7and6.and the key nuber is 14 because 3+8+7+6=24-10=14
5)in the 5th room there are 19 tarts because 4x4+3= 19 and 6x3 = 18 +1=19 so the key number is 19,

using the code a=1 b=2 c=3 z=26 etc.you get the letters m i o n s
and the finished anagram is Simon .
Thats how you escape the castle.