## A Tale of Two Banks and the “Three Friends Go Out to Lunch” Brain Teaser

I recently had two separate conversations with two different people, both in banking.

One is a VP at a Regional Bank in California. The other is the CEO of a bank based on the Middle East, growing by expansion and acquisitions. Two different worlds, night and day. Both deal with loans and try to mange risk while trying to grow. But the similarities end quickly.

After the conversations, I was reminded of the following “Three Friends go out to Lunch” problem I read years ago in some brain teaser book. Enjoy! My response is here.

Three friends go out to a restaurant and order three lunch specials. The bill comes out to $30 (with tax, no tip). They decide to leave $10 each. As they leave out the door, the owner realizes that the bill was incorrectly calculated: it should have been $25 including tax. He sends the waiter out with five one dollar bills. The waiter, feeling slighted by not having received a tip, keeps $2 and gives a dollar bill to each of the the three friends.

So each friend paid $9 (originally paid $10 each, but each got a dollar back). The waiter keeps $2. Three times $9 is $27, plus the two dollars is $29. Where is the other dollar?

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## Comments

This is more of an “accounting” problem than a “math” problem. The statement, “Three times $9 is $27, plus the two dollars is $29.” and the subsequent question, “Where is the other dollar?” are misleading. We are incorrect in adding the $27 and the $2.

The key to understanding what’s happening is by thinking thru the three entities and their “accounts”. It’s a good illustration, IMHO, of some of the differences between “math” and “accounting”.

Anyone want to bother doing the T-Accounts?

I never understood the confusion of the problem other than the sleight of hand of “3×9=27+2=29”.

Each paid $27 and the waiter took $2. $27-2=25. That is what the owner got. The fact that 30 was involved earlier is just a distraction.