Imagine you and two friends are eating at your favorite restaurant on a Friday night. The check is $30, and you all agree to split it evenly—$10 per person. It’s a fun night: you’re laughing and chatting, and the bill is the last thing on your mind. Later, the restaurant manager realized that a promotional discount had been overlooked, and the actual bill should have only been $25. Realizing the error, he quickly hands the waiter $5 to return to the table.
As the waiter walks to your table, he realizes that $5 can’t be divided equally, so he discreetly pockets $2 as a tip for himself and gives each of you $1 back. That means instead of paying the original $10 each, you now pay $10 – $1 = $9 per person. So together, you all paid $9 x 3 = $27.
But don’t forget about the $2 the waiter kept. If you factor that in, you get $27 + $2 = $29. But hold up—a minute ago, you paid $30 for everything, and now it’s $29. Where is the missing dollar?
As it turns out, no dollar is missing. The confusion comes from the way the numbers were crunched. Think about it like this: the $27 we paid already includes the waiter’s $2 tip. So rather than adding $2 to our side, we should add it to the restaurant’s side. Remember, the restaurant manager wanted to refund us $5, but only $3 ever made it into our hands. The other $2 is still with the restaurant (in the waiter’s pocket). Therefore, we paid $9 + $9 + $9 = $27 = $25 + $2. See? Nothing was lost!
This little puzzle isn’t just a cute math trick—it’s also a great example of how we sometimes mix up our numbers and perspectives in everyday life. Consider a trial where a defendant is accused of being in two places at once on the night of an incident. The prosecutor lays out a timeline that, at first glance, seems to show an unexplained gap. Then the defense attorney steps in. Instead of presenting the entire timeline, he highlights only those details that support his client’s alibi. He points out the periods when witnesses saw the defendant at locations that match the defense’s version of events but omits the security camera footage that fills in the missing time. By leaving out that crucial detail, the defense creates the impression that there’s a gap in the timeline, which
Hi—I’m Andy Tang, a Schreyer Scholar at Penn State double-majoring in computer science and economics. Most days you’ll find me happiest in front of a code editor, turning data and ideas into working projects. When the laptop closes, I trade topspin rallies on the table tennis court or head to the basketball court to perfect my mid-range hook shots.
This e-portfolio stitches those interests together. You’ll hear my This I Believe podcast on charcoal and honesty, read a civic artifact essay about how strategy games captured pandemic attention, and dive into a paradigm shift piece tracing goth music’s evolution. Explore, enjoy, and feel free to reach out if something sparks a conversation.