Potato Paradox Calculator

Explore the famous math puzzle: a small change in water percentage leads to a surprisingly large change in weight.

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The Classic Puzzle

You have 100 kg of potatoes that are 99% water. After drying, they become 98% water. How much do they weigh now? (The answer is surprisingly NOT 99 kg!)

Result

Final Weight
50
kg
Initial Weight 100 kg
Initial Water Weight 99 kg
Solid (Non-Water) Weight 1 kg
Final Weight 50 kg
Final Water Weight 49 kg
Weight Lost 50 kg (50%)

Step-by-Step Solution

Final Weight = Solid Weight / (1 - Final Water %)

The Potato Paradox Explained

The Potato Paradox is a famous mathematical puzzle that demonstrates how our intuition about percentages can be wildly misleading. The classic version goes: "You have 100 kg of potatoes, which are 99% water. You leave them in the sun, and they dry until they are 98% water. How much do they weigh now?" Most people guess around 98 or 99 kg, but the correct answer is 50 kg -- a loss of half the total weight from just a 1% change in water content!

Why It Works

The Key Insight

The solid matter stays constant. Only water evaporates. The percentage refers to the ratio, not an absolute amount.

Solid = Weight x (1 - Water%)

The Formula

Since solids remain constant, the new total weight is determined by the new water percentage.

New Weight = Solid / (1 - New%)

The Surprise

Going from 99% to 98% water means solids go from 1% to 2% of total -- that is a doubling of solid proportion!

1% to 2% = halving total weight

Mathematical Explanation

Let us work through the classic problem step by step:

  1. Start with 100 kg potatoes that are 99% water.
  2. Water weight = 99% of 100 = 99 kg.
  3. Solid weight = 1% of 100 = 1 kg.
  4. After drying, potatoes are 98% water. The solid weight (1 kg) has not changed.
  5. If solids are now 2% (100% - 98%) of the total, then: 1 kg = 2% of total.
  6. Total = 1 / 0.02 = 50 kg.

Why Our Intuition Fails

We instinctively think "1% change = small change." But when dealing with very high percentages (like 99%), a 1% decrease in water means the non-water portion doubles (from 1% to 2%). Since the solid mass is fixed, the total weight must halve to make the solid proportion double. This is a form of base rate neglect -- we focus on the small absolute change (1%) rather than the large relative change in the solid component (100% increase).

Real-World Applications

  • Food science: Dehydration and moisture content in food preservation.
  • Statistics: Understanding how small percentage changes can have large effects.
  • Finance: Similar paradoxes appear in profit margins and markup calculations.
  • Medicine: Drug concentration changes in body fluids.