Zetamac Strategies

Zetamac is widely-known website in the quant space, designed as a benchmark for mental math speed.

The format, 120s to solve as many addition, subtraction, multiplication, and division problems.

My motivation, my brother challenged me and I don't back down, but also mental math is one of the best bang for buck skills in real-life. Calculate your groceries tax? Estimate your restaurant bill?

My goal on the site is to hit 100 problems in 120s. My current best is 86.

I even build my own version of zetamac! But this one records your performance and has a competitive leaderboard! I'm buying anyone who beats my score a free bbt (given you're at waterloo).

Check it out, https://datamac.vercel.app/.

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

This is the easiest type of problem in Zetamac. Primarily because our brains are so accustomed to them. The key strategy is to sum digits from left to right, which may seem counterintuitive to the typical way we were taught in school. Why? 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 subtraction problems, I use the same left-to-right strategy as addition, and being clever about carry overs.

Strategy 1: Direct Subtraction

Work from left to right, 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 (my preference)

Break the problem into easier parts.

Example:

For 9 × 74:

This is sometimes faster since addition is less brain-intensive than subtraction. But you need to know your 12x12 time table flawlessly.

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

Final Remarks:

There's absolutely no substitude for putting hours of practice, this is how your brain gets used to pattern recognition, and hence becomes faster. You'll see how useful these skills are in day-to-day life, have fun with it!