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Eleven cards are numbered from 1 to 11, one number per card. For how many pairs of cards is the sum of the two numbers a prime number?

Oct 14, 2020

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11C2 = 55 combinations.

[(1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (1, 10), (1, 11), (2, 3), (2, 4), (2, 5), (2, 6), (2, 7), (2, 8), (2, 9), (2, 10), (2, 11), (3, 4), (3, 5), (3, 6), (3, 7), (3, 8), (3, 9), (3, 10), (3, 11), (4, 5), (4, 6), (4, 7), (4, 8), (4, 9), (4, 10), (4, 11), (5, 6), (5, 7), (5, 8), (5, 9), (5, 10), (5, 11), (6, 7), (6, 8), (6, 9), (6, 10), (6, 11), (7, 8), (7, 9), (7, 10), (7, 11), (8, 9), (8, 10), (8, 11), (9, 10), (9, 11), (10, 11)],  >Total distinct combinations = 55

(3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 5, 6, 7, 8, 9, 10, 11, 12, 13, 7, 8, 9, 10, 11, 12, 13, 14, 9, 10, 11, 12, 13, 14, 15, 11, 12, 13, 14, 15, 16, 13, 14, 15, 16, 17, 15, 16, 17, 18, 17, 18, 19, 19, 20, 21)>Total = 55 sums

(3, 5, 5, 7, 7, 7, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 17, 17, 17, 19, 19)>>Total = 21 pairs are prime numbers

Oct 14, 2020