Take 100 pounds of potatoes that are 99% water. If they dry out until they are 98% water, instinct screams they should weigh 99 pounds. In reality, the sack now weighs exactly 50 pounds.
Our brains are spectacularly bad at intuitively grasping ratios when the underlying numbers shift, which is why this puzzle—known as the Potato Paradox—routinely tricks even experienced mathematicians. Letting the potatoes drop from 99% to 98% water concentration caused them to lose half their total mass.
The illusion breaks when you stop looking at the water and start looking at the solid material. When you begin with 100 pounds of potatoes that are 99% water, you have 99 pounds of water and 1 pound of solid, dry potato matter.
As the potatoes sit in the sun, only the water evaporates. The solid mass stays exactly the same. You still have exactly 1 pound of solid potato. The puzzle states that after drying, the potatoes are now 98% water. That means the solid matter must now make up the remaining 2% of the total weight.
If 1 pound of solid mass represents 2% of the total weight, the math becomes straightforward. 1 pound is 2% of 50 pounds. Therefore, the total weight of the sack must be 50 pounds. The new sack contains 49 pounds of water and 1 pound of solid matter (which still equals 50 pounds, with the water making up 98%).
The paradox works because our brains anchor to the initial 100 pounds and assume a small change in water percentage equates to a small change in total weight. In reality, shifting a concentration from 99% to 98% means the proportion of solid matter doubled from 1% to 2%. To double the concentration of a fixed amount of solid matter, the total mass of the object must be cut in half.