8 people total, so

A: max handshakes = 6 (not self, not spouse)

B: min handshakes = 0 (negative shakes not possible)

When the guy asked 7 other people how many handshakes,

they all gave different answers, so those answers must be

0, 1, 2, 3, 4, 5, 6 (no other numbers are possible)

Let's designate the 8 people by the number of handshakes with L for Mr. Lewis: L 0 1 2 3 4 5 6 

6 shook hands with L,1,2,3,4,5, so his/her spouse is 0

1 shook hands with 6, that uses up his quota.

0 // done

1 with 6 // done

2 with 6, and 1 more

3 with 6, and 2 more

4 with 6, and 3 more

5 with 6, and 4 more

L with 6, and ? more

Now 5 has to shake with 4 more and they must be 2,3,4,and L

becaue noone else is available.

0 // done

1 with 6 // done

2 with 6, 5 // done

3 with 6, 5, and 1 more

4 with 6, 5, and 2 more

5 with 6, L, 2, 3, 4 // done

6 with L, 5, 4, 3, 2, 1 // done

L with 6, 5, and ? more

Now we do 4, his two additional must be 3 and L

0 // done

1 with 6 // done

2 with 6, 5 // done

3 with 6, 5, 4 // done

4 with 6, 5, 3, L // done

5 with 6, L, 2, 3, 4 // done

6 with L, 5, 4, 3, 2, 1 // done

L with 6, 5, 4 // done

and that's all the shakes, everyone has used up their quota,

so noone left to shake with L

6 and 0 are spouses

only person left with whom 5 did not shake is 1, so that's his/her spouse

that leaves 2,3,4 and L

4 shook with 3 and L, so 4 must be 2's spouse

and therefore L's wife is 3 and he also shook 3 hands.