Liberty Math Club

The Estimathon

The Estimathon is a team contest in estimation. Teams have 30 minutes to answer 13 questions whose exact answers almost no one knows, such as how many gas stations in the United States have a convenience store. Instead of a single number, each answer is a range. A narrow range that contains the true value scores well. A range that misses costs a team a great deal.

No calculus or advanced mathematics is needed. The contest rewards reasoning about size, sensible assumptions, and teamwork.

Format

• Teams have 2 or 3 people. A team may include at most one professor.
• Each team receives the same 13 questions and has 30 minutes.
• Every answer is a positive number. A team answers with an interval, a minimum and a maximum, such as [2,000, 8,000]. Both ends must be positive.
• Each team has 18 answer slips. A slip lists the team name, the question number, and the interval. Slips can be turned in at any time during the 30 minutes.
• A team may answer the same question more than once. Only its last slip for that question counts, whether it was right or wrong.
• A scoreboard updates during the contest as slips are graded.

Rules

• No calculators, phones, internet, or other reference material.
• Paper, pencils, and teammates are allowed.
• An interval is good if it contains the correct answer.
• The team with the lowest score wins.

Scoring

Each good interval earns points based on how wide it is: divide the maximum by the minimum, round up, and subtract 1. A perfect guess scores 0. A team's total is

Score = (10 + P) × 2^M

where P is the sum of the points from all good intervals and M is the number of questions without a good interval, whether missed or left blank. Each of those doubles the score, so a wide range that is right usually beats a narrow range that is wrong.

For example, a team with good intervals on 11 questions earning 39 points in all, and 2 questions missed, scores (10 + 39) × 2² = 196.

Tips

• Break a question into pieces you can estimate, such as people, rates, and time, and multiply.
• Think in powers of ten first. Being within a factor of 10 is a good start.
• Answer every question. A blank question doubles the score just as a wrong one does.
• Save a few slips. Use them to fix a missed question or to narrow a range once the team agrees.

Practice questions

Give a range for each, then open it to check. Try to keep every range within a factor of 2 or 3.