Find the number of positive integer pairs x,y which satisfy the equation 3x+2y=100 ?

If there is not a mathematichal trick, the pairs are :

X Y
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2 47
4 44
6 41
8 38
10 35
12 32
14 29
16 26
18 23
20 20
22 17
24 14
26 11
28 8
30 5
32 2

100 cards are numbered 1 to 100 (each card different) and placed in 3 boxes (at least one card in each box). How many ways can this be done so that if two boxes are selected and a card is taken from each, then the knowledge of their sum alone is always sufficient to identify the third box?