Today my MathCounts team practiced their first Countdown Round. This is the spelling bee style competition in which students compete head-to-head on stage to answer the question before their opponent. Identifying elegant shortcuts is critical to getting the answer asap. For example:
(Source: 2016 MathCounts Chapter Countdown Round)
The question asks for the difference between the average time and 10 minutes. While one could find the average of the 3 times and then subtract from 10 minutes, a more clever approach (using smaller numbers) is to average the 3 differences from the start. Since , . The other time differences are and . The sum is and the average is Smaller numbers means quicker, more accurate calculations.