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The Potato Paradox

A tiny change in water percentage causes a massive change in weight

🥔 Test Your Intuition

Fred brings home 100 kg of potatoes.
They are 99% water.
He leaves them outside overnight to dry.
Now they are 98% water.

What is their new weight?
kg

Before: 99% Water

100
kg
💧 99 kg water + 1 kg solid

After: 98% Water

?
kg
💧 ? kg water + 1 kg solid

The Mathematics

Step 1: Find the dry mass

If potatoes are 99% water, they're 1% solid matter.

Dry mass = 100 kg × 1% = 1 kg

Step 2: The key insight

Only water evaporates. The 1 kg of dry mass stays constant!

Dry mass before = Dry mass after = 1 kg

Step 3: Set up the equation

After drying, the 1 kg dry mass must be 2% of total (since 98% is water).

1 kg = 2% × Total weight

Step 4: Solve!

If 1 kg = 2% of total, then total = 1 kg ÷ 0.02

Total weight = 1 kg ÷ 0.02 = 50 kg

Step 5: Verify

50 kg total - 1 kg dry = 49 kg water

49 kg ÷ 50 kg = 98% water ✓

Visual Mass Comparison

Before (100 kg)
Water: 99 kg
1
100 kg
After (50 kg)
Water: 49 kg
1
50 kg
50 kg water evaporated
50% total weight lost
1 kg solid (unchanged)

Weight Calculator

Try different starting values and see the surprising results!

Final Weight:
50 kg

Step-by-Step Calculation

1
Calculate dry mass (constant)
Dry mass = 100 kg × (100% - 99%) = 100 × 0.01 = 1 kg
2
Calculate initial water mass
Water = 100 kg × 99% = 99 kg
3
Set up final weight equation
If final is 98% water, then dry mass = 2% of final weight
1 kg = 0.02 × Final Weight
4
Solve for final weight
Final Weight = 1 kg ÷ 0.02 = 50 kg
5
Calculate water evaporated
Final water = 50 kg × 98% = 49 kg
Water lost = 99 kg - 49 kg = 50 kg evaporated

Why Is This So Counterintuitive?

Our brains see "99% → 98%" and think "lost 1% of water." But that's not what happened! The percentage changed, not the absolute amount of water lost.

The Key Insight: When water evaporates, you're removing weight from BOTH the numerator (water) AND the denominator (total weight). The ratio changes much faster than you'd expect!

Think of it this way: at 99% water, the dry matter is just 1% of total weight. At 98% water, dry matter must be 2% of total weight—that's double the proportion! Since the dry mass (1 kg) can't change, the only way to double its proportion is to halve the total weight.

Real-World Applications

This isn't just a mathematical curiosity. The potato paradox applies to:

The Martian Connection: In "The Martian," Matt Damon's character grows potatoes on Mars. If he harvested them at 99% water and they dried to 98% in the thin atmosphere, he'd lose HALF his food supply—not 1%!

This is classified as a veridical paradox—a result that seems absurd but is demonstrably true. The math is simple algebra; the surprise comes from our poor intuition about how percentages work with changing totals.