#### Answer

$$341$$
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Let us perform the operations according to the suggested algorithm. We'll
keep track of the total number of matches after each round. We start with
342 players and divide them by two, which will give us the number of winners
in each given round. In case of an odd number of players, the leftovers will
only play in the round after that.
1. $342 / 2=171$ matches $[171 \text { total }]$
2. $171 / 2=85$ matches plus 1 left over $[256 \text { total }]$
3. $86 / 2=43$ matches $[299 \text { total }]$
4. $43 / 2=21$ matches plus 1 left over $[320 \text { total }]$
5. $22 / 2=11$ matches $[331 \text { total }]$
6. $11 / 2=5$ matches plus 1 left over $[336 \text { total }]$
7. $6 / 2=3$ matches $[339 \text { total }]$
8. $3 / 2=1$ match and 1 left over $[340 \text { total }]$
9. $2 / 1=1$ final match between the last 2 remaining players ${[341] \text { total }}$
After 9 rounds we got to a total of 341 matches needed to determine a
winner.

#### Work Step by Step

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