Guide
A guide to estimating big numbers
Most people believe they are bad at guessing numbers. In truth they are bad at one thing: they guess linearly when the world is multiplicative. Fix that, and almost every Catamount question gets easier.
1. Think in orders of magnitude first
Before you worry about the digits, decide how many digits. Is the answer in the tens, the hundreds, the thousands, the millions? Getting the order of magnitude right is most of the battle, because a guess that is the right size is within a factor of ten, and a good bracket brings you within a factor of two or three.
For example: how tall is a typical skyscraper like the Willis Tower in Chicago? Nobody carries that number in their head. But you know a tall building has about 100 floors, and a floor is about 10 to 13 feet. That is somewhere between 1,000 and 1,300 feet, and the real figure is about 1,450 feet to the roof. You were never going to get the exact number, and you did not need to.
2. Bracket, then take the geometric middle
Ask yourself two questions: What is the smallest number that I would be shocked to see? and What is the biggest? Those are your bounds. Now pick the middle, but the right kind of middle.
The ordinary average of 100 and 10,000 is 5,050, which is only half of the upper bound and looks nothing like a compromise. The geometric middle is the number that is as many times bigger than the low bound as it is smaller than the high bound: here, 1,000. To get it, multiply the two bounds and take the square root, or just ask "what is halfway in digits?" Because Catamount scores by ratio, being twice too high costs the same as being twice too low, so the geometric middle is the guess that treats both mistakes fairly.
3. Collect anchor facts
Good estimators do not know everything. They know a few dozen numbers very well and build everything else from them. Here is a starter set, all of them rounded:
| Anchor | Value |
|---|---|
| Circumference of the Earth | About 24,900 miles |
| Distance to the Moon | About 239,000 miles |
| Distance to the Sun | About 93 million miles |
| Speed of sound | About 760 mph |
| Cruising speed of a jetliner | About 550 to 575 mph |
| Highest mountain (Everest) | About 29,000 feet |
| A marathon | 26.2 miles |
| US population | About 340 million |
| World population | About 8 billion |
| Days in a year / minutes in a day | 365 / 1,440 |
With those in hand, a question like "how many times could you drive around the Earth on a tank of gas" turns into arithmetic, and a question about a flight time becomes distance divided by 550.
4. Build it from pieces
When you know nothing about the target, break it into things you do know. This is called a Fermi estimate, after the physicist Enrico Fermi, who loved asking questions like how many piano tuners are in Chicago. The trick is that errors in the pieces tend to cancel: you will round some up and some down, and the total is better than any single guess. Do not try to be precise with the pieces. Be roughly right with each.
5. Watch the units and the date
Many bad guesses are a unit mistake in disguise. Catamount shows the unit next to the keypad, and it is worth glancing at before you commit. A question about meters, miles and feet can have answers that differ by a factor of three or five without any of them being wrong. Dates matter too: a price "at launch" is a price from a specific year, and a record is a record as of a given date.
6. Mind the clock, but not too much
The speed bonus is at most 8 percent of a question's score. Spending 12 seconds to bracket well is almost always worth more than saving 8 seconds. Use the first few seconds to decide the order of magnitude, then refine.
7. Learn from the reveal screen
After each answer Catamount shows the true value and a short note on where it comes from. That note is the best part. Over a few weeks of daily climbs, you will build up exactly the anchor facts that matter. Our fact files collect many of them by category.