Zetamac Strategies

Zetamac is widely-known website in the quant space, designed to test for mental math speed. The format, 120s to solve as many addition, subtraction, multiplication, and division problems.

My motivation behind it, primarily because my brother challenged me but also I think it's a fun and useful skills that is applicable day-to-day. Want to prematurely calculate your groceries tax? Want to estimate your restaurant bill after tax and tip, so you can confront the waiter otherwise? Mental math is the way to go!

My goal on the site is to hit 100 problems in 120s. My current best, 65.

I even build my own version of zetamac! But this one tracks performance, graphs it, and has a community leaderboard! Check it out, https://datamac.vercel.app/.

Now, I'll outline some of the strategies I've learned so far so you too can get faster :)

This is the easiest type of problem in Zetamac. Primarily because our brains have done so many of these, compared to others like subtraction. The key strategy is to sum digits from left to right, which is always faster than right to left. This approach allows you to start typing the answer immediately while simultaneously calculating for the next digit.

The Strategy:

Example Walkthrough:

For 38 + 55:

1. I know it should start with an 8 (3+5)

2. Then I see the ones digits sum to 13 (8+5)

3. So I quickly change my answer to 93

This method is faster because you can begin typing while still processing the remaining digits.

Subtraction is a bit trickier than addition but follows similar principles. For 2-digit subtract 2-digit problems, I use the same left-to-right strategy as addition, and being clever about carry overs.

Strategy 1: Direct Subtraction

Work from right to left, handling carry overs as they come.

Strategy 2: Complement Method

Instead of subtracting, think about how much you need to add to the smaller number to get the larger value.

Example Walkthrough:

For 83 - 69:

For 3-digit subtract 2-digit:

1. Determine what you need to add to the 2-digit number to make it 100

2. Then determine from 100 how much you need to add to get the 3-digit number

Example:

For 132 - 79:

1. I know I need 21 to make 79 become 100

2. Then I add 21 + 32 = 53 to get my answer

Most single-digit multiplication problems can be solved by rounding the second number to a nice value, then subtracting or adding as needed.

Strategy 1: Rounding Method

Round one number to make the calculation easier, then adjust.

Example:

For 9 × 74:

Strategy 2: Breaking Down

Break the problem into easier parts.

Example:

For 9 × 74:

This is sometimes faster since addition is less brain-intensive than subtraction.

The 11 Trick:

When multiplying by 11, add the digits of the second number and insert that value in the middle.

Example:

For 11 × 63:

With Carry Over:

For 11 × 84:

Why This Works:

11 × 63 = 10 × 63 + 63 = 630 + 63 = 693

The middle digit is the sum of the original digits because we're adding the number to its 10x version.

When both numbers are two digits, the strategies become more complex but still manageable with practice.

Strategy 1: Breaking Down by 10s

Break the first number into 10s and units, then multiply each part.

Example:

For 12 × 45:

Strategy 2: The 12 Trick

For 12 × any number:

Memorization Strategy:

For smaller numbers, memorize sequences of multiples:

Example:

For 540 ÷ 12:

Important Note:

These strategies work because Zetamac ensures results are always integers, so these rules aren't generalizable to all values.

Division in Zetamac can be made much faster with specific tricks for common divisors.

The 11 Division Trick:

When dividing by 11, the answer is either the two outer digits, or (due to carry over) the two outer digits with the leftmost digit reduced by 1.

Example 1 (No Carry Over):

374 ÷ 11 = 34

Example 2 (With Carry Over):

974 ÷ 11 = 84

The 9 Division Trick:

For 3-digit numbers divided by 9:

1. First digit = floor(first two digits ÷ 9)

2. Second digit = 10 - last digit

Example:

342 ÷ 9 = 38

Why This Works:

The first digit represents how many times 9 goes into the two most significant digits, and the second digit is 10 minus the least significant digit.

General Strategy:

Memorize sequences of multiples for common divisors to quickly identify patterns and solutions.