Answer: a star (read Sun)

Remark: Sun does not actually burn. Its heat and light come from procces called nuclear fusion (smashing small light elements together to make heavier elements; most of a star’s life is spent smashing hydrogen atoms together to make helium). So the “burning” that Sun does is nucler reaction, while the burning on Earth (one we all think of when we hear word burn) is chemical process that requires oxygen (there is no oxygen in outer space).

Answer: 71842

Solution:
a b c d e (digits of given number)
2 prime digits
9 >= c > a, d, e > b >= 1
a > d + e
e = d/2
a = c – 1
b < e = a+1 > a, e, 2e > b >= 1
a > 2e + e = 3e

Answer: 1 time

Solution: Coins are of the same size so they have same circumference.

Answer: 14285

Solution: Let that five digit number be x. Then the number we get when we add 7 at the beginning is 700000 + x and the number we get when we add 7 at the end is 10x + 7. Now we need to solve simple equation:
700000 + x = 5 * (10x + 7)
700000 + x = 50x + 35
699965 = 49x
x = 14285
So five digit number is 14285 (142857*5 = 714285).

Answer: He bought 9 of 3p and 9p and 8 of 11p, 17p and 21p stamp dominations.

Solution: Sum of 8 of all stamp dominations is 8*(3+9+11+17+21) = 488, which means that there are 12p left and only way is to use one 3p and one 9p. So he bought 9 of 3p and 9p and 8 of 11p, 17p and 21p stamp dominations ( 9*(3+9)+8*(11+17+21) = 108 + 392 = 500 ).