If 32 teams participate in a standard single elimination tournament, how many games must be played to decide a champion?

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Explanation:

Count the number of times you divide by two and we have five occurrences of this. So there five rounds overall.

To get the total number of games played, we add up the quotients

16+8+4+2+1 = 31

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Or as a shortcut we can simply subtract off 1 since 1+2+4+...+2^n = 2^(n+1)-1

We can write that rule as

which is equivalent to

when the daily mileage is greater than 40 miles, unlimited mileage plan will save you money. 40 miles is the break-even point.

step-by-step explanation: