Question

Please find how to get answer of attachment below.

Answer 1

The 52th card that was dealt was an 8.

Explanation:

The total value of the entire deck is
`4(1 + 2 + \cdots + 9 + 10 \cdot 3) = 4((10 \cdot 11)/(2) + 20) = 220 + 80 \equiv 0 \mod 10.`

The total value of the 51 cards face-up is congruent to
`0 + 3 + 6 + 1 + 10 + 10 + 4 + 8 = 42 \equiv 2 \mod 10.`

The 52th card must therefore be an 8 for the total value of the entire deck to be 8 mod 10. (Or, rather, we have that the last card must be
`0-2 \equiv 8 \mod 10` and the only card that is congruent to that value modulo 10 is the 8.)