Answer:
Total number of matches played were 15
Step-by-step explanation:
Data provided in the question:
Number of competitors = 16
The tournament is a single elimination tournament
paired competitors played matches and only the winner of a match continued to the next round
therefore,
Dividing 16 competitors in pairs, there will be 8 pairs.
as each pair plays 1 match
Thus,
8 matches ............(a)
Now,
winner of 8 matches will be 8 competitors
Further, dividing the 8 competitors in pairs, there will be 4 pairs.
as each pair plays 1 match
Thus,
4 matches ............(b)
Further, dividing the 4 competitors in pairs, there will be 2 pairs.
as each pair plays 1 match
Thus,
2 matches ............(c)
now, the winner of the 2 matches will be 2 competitors,
thus, 1 more match to decide the winner.
thus,
1 match .............(d)
adding (a), (b), (c) and (d)
we get
8 + 4 + 2 + 1 = 15 matches
Hence,
Total number of matches played were 15
