Total number of ways to make a pair:
The first player can be any one of 7 . For each of those . . .
The opponent can be any one of the remaining 6 .
Total ways to make a pair = 7 x 6 = 42 ways .
BUT ... every pair can be made in two ways ... A vs B or B vs A .
So 42 'ways' make only (42/2) = 21 different pairs.
If every pair plays 2 matches, then (21 x 2) = <em><u>42 total matches</u></em> will be played.
Now, is that an elegant solution or what !
I suppose you want to know such number. Since we have a two digit number consisting of two consecutive integers, the only possible numbers are:

Since we sorted all the cases out, we simply have to check which one satisfies the requirement. For each number, we'll write four times the the sum of its digits, and add 6, hoping to get the original number.



So, the answer is 34.
Answer:

will give you an explanation if you want tag me on comment.
139, 149, 159, 169, 179, 189, 199, 209, 219, 229, 239, 249, 259.
The common difference is 13.
Let n = 52
Let d = common difference
a_52 = 139 + (52 - 1)(13)
a_52 = 139 + (51)(13)
a_52 = 139 + 663
a_52 = 802