Puzzles
15 December
When talking to someone about this Advent calendar, you told them that the combination of XMAS and MATHS is GREAT.
They were American, so asked you if the combination of XMAS and MATH is great; you said SURE. You asked them their name; they said SAM.
Each of the letters E, X, M, A, T, H, S, R, U, and G stands for a different digit 0 to 9. The following sums are correct:

 
Today's number is SAM. To help you get started, the letter T represents 4.
24 December
There are six 3digit numbers with the property that the sum of their digits is equal to the product of their digits. Today's number is the largest of these numbers.
15 December
There are 5 ways to make 30 by multiplying positive integers (including the trivial way):
 30
 2×15
 3×10
 5×6
 2×3×5
Today's number is the number of ways of making 30030 by multiplying.