Meredith Math

The classic Monty Hall Problem:

You are on a game show. There are three doors for you to choose from. Behind two doors are goats- choosing one of these gets you nothing.

Behind the other door is the keys to a new car!

You make your selection. But, before you see what is inside, the game show host (who knows what's behind each door) opens one another door, revealing a goat.

He then gives you the option to change your choice. There are two doors remaining: your original choice, or the other closed door.

Should you swap?

Most people believe it doesn't matter if you change or not. They think there's two doors, so it is 50/50. But that's not true!

By choosing to swap from your original choice to the last door, you up your chances of winning a car to 2/3! By staying, you have only a 1/3 chance of winning. Pretty unintuitive. It sounds fake, but it is very true.

Three people pay $30 (or $10 each) for a room. Later, the clerk realizes the room should have cost $25, so $5 is sent back. The bellhop gives each person $1 and keeps $2.

Now each person paid $9, totaling $27. The bellhop kept $2. That makes $29.

Where is the missing dollar?

Another example in the same vein of the WW2 survivorship bias:

A recent poll indicated that 100% of people enjoy responding to unsolicited polls

You may think that numbers in real-world data are pretty equally random.

This is not the case!

When looking at any type of data, from finance and business to scientific experiments, the first digit in each number is over 7 times more likely to be a 1 than it is a 9.

Low numbers show up as the leading digit much more often than high numbers.

This fact is actually used by the IRS and forensic accountants to detect fraud! Humans trying to deceive will attempt to mix things up pretty evenly, not following how the numbers would really look if it was real data.

This phenomenon is known as Benford's Law.

Meredith Math

In World War 2, the biggest brains were deciding where they ought to armor their planes to improve survivability across enemy lines.

Naturally, they observed the returning planes to see where they were being shot. The image shows the average hotspots where heavy fire was observed.

They clearly realized they should armor the center, the wings, and the tail, as that's where the planes were being hit most.

But wait!

Brilliant statistician Abraham Wald realized something critical:

These planes survived!

The planes that were hit in the engines, cockpit, and critical systems never made it home to be analyzed.

A brilliant example of how mathematical thinking can change how you come to all sorts of conclusions, and eliminate biases- in this case, this is known as Survivorship Bias. There are many, many cases in life similar to this one.

I want to help your teen unlock their academic potential. Boosting their math scores for their college entrance exams can put them one step closer to unlocking scholarships, admittance to their dream schools, and, ultimately: their dreams!

When you think of math, you may not think of little logic puzzles like this. Logic, though, is the grandfather of all math.

The higher you go, it's less about being able to plug numbers into equations, and more about understanding why those equations work in the first place.

This makes mathematics a valuable tool to teach critical thinking that applies to all facets of life: take a system down to its bare parts, and see how they interact with each other. It's exercise for your brain. It's a thought process that's useful no matter what you do.

Those same skills can be trained through little puzzles like this one!

Tutoring is more than homework help—it’s building habits and skills that lead to scholarships and college readiness.

Scholarships can save families thousands. A small investment in tutoring now can make a big difference later.