101
【Solution】Solution: According to the analysis, the face value of the two hearts must be no less than $1+2=3$; if the face value of the hearts is not less than 4, according to the problem, the face value of the spades is not less than 44, but the maximum face value of the spades is $11+12+13=$ $36<44$, which is a contradiction;

Therefore, the face value of the hearts is 33, and similarly, it is easy to know that the face value of the diamonds is not less than $1+2+3+4=10$, from which we know that the face value of the clubs is not less than $10+45=55$,

and the maximum face value of the clubs is $9+10+11+12+13=55$;
Therefore, only the face value of the diamonds being 10 and the face value of the clubs being 55 meets the conditions.
In summary, the sum of the face values of the 14 cards is: $3+33+10+55=101$.
Therefore, the answer is: 101.
7. (10 points) A deck of playing cards, excluding the jokers, has 4 suits totaling 52 cards, with each suit having 13 cards, numbered from 1 to 13. Feifei draws 2 hearts, 3 spades, 4 diamonds, and 5 clubs. If the sum of the face values of the spades is 11 times the sum of the face values of the hearts, and the sum of the face values of the clubs is 45 more than the sum of the face values of the diamonds, then the total sum of the face values of these 14 cards is _