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Let \(a, b, c, d\) and \(e\) be the numbers of 1 cent, 5 cent, 10 cent, 25 cent and 50 cent coins, respectively.
Then \(a + 5b + 10c + 25d + 50d = 50.\)

The possible numbers of each coin are as follows:
(a,b,c,d,e) = (50,0,0,0,0) : 50 coins
(a,b,c,d,e) = (45,1,0,0,0) : 46 coins
(a,b,c,d,e) = (40,2,0,0,0) : 42 coins
(a,b,c,d,e) = (40,0,1,0,0) : 41 coins
(a,b,c,d,e) = (35,1,1,0,0) : 37 coins
(a,b,c,d,e) = (30,2,1,0,0) : 33 coins
(a,b,c,d,e) = (30,0,2,0,0) : 32 coins
(a,b,c,d,e) = (25,1,2,0,0) : 28 coins
(a,b,c,d,e) = (25,0,0,1,0) : 26 coins
…
Only 41 and 26 are in this list.
Therefore, the answer is D.

Answer: D
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