# Outsmarting a Con (sales) man

During a fun filled golf event vendors have set up stalls offering different things to participants like golf gear, food, clothing etc. Participants can also win gifts in putting contests, drives and other fun things.

A smart salesman has set up his stall for selling golf balls. He has either yellow or white standard golf ball boxes. Example below of a 1 dozen box. Ignore two outside balls.

He then tells interested folks: “This is a -guess the boxes in the bag- game. In front of you are two opaque paper bags. (Example above). I am going to put one golf box in each of them in any order. They will be of one color only. Here is what I have:

Box A and Box B: 1 Dozen White Balls each.

Box C: 3 Dozen White Balls.

Box D: 3 Dozen Yellow Balls and

Box E: 6 Dozen Yellow Balls

Five boxes total. The 2 opaque bags will have 2 of the (same color) 5 boxes in any order. Each bag will have only one box. Here is how this game goes.

First, you pick any box out of the five you want. You will know which one it is. It is yours if you guess what is in any of the 2 bags correctly. If you guess the contents of both the bags correctly you get all the five boxes. Your guess must identify the boxes correctly with color and how many dozens in the box.

I am going to make it easy for you. I will only put the same golf ball color boxes in both the bags while you are not looking. If the first bag has white golf balls the second one will too. So you have a great chance of winning.If you do not guess right then all you have to do is to buy the box you picked first for mere 50 dollars per dozen”

Folks were going for it. Once in a while someone would guess one bag correctly but not often. The salesman sold a lot of golf balls.

A smart golfer was watching. She goes to him and says: “I can guess both the bags correctly. I have a special skill. If I do not, I will buy ALL the five boxes for 100 dollars a dozen. If I do, then you give me all the five boxes AND \$50.”

The salesman smiled. “What special skill do you have?”

“I have a great sense of golf ball smell!”

Everybody laughed. The salesman said: “So you are going to smell the bags?”

“Not both. I will just smell the first bag and give you the answer. Are you in?”

All watchers started cheering. The salesman went for it. He asked her which box she wants. She chose one (of the five). He handed that box to her. Then he secretly put two other same color boxes in the 2 bags keeping the remaining 2 out of sight. Bags were opaque and he sealed the tops tightly.

The woman then picked one of the bags from the top and smelled it. She did not peek or cheat. Then she guessed the contents of the 2 boxes correctly.

How did she do that? What strategy gave her 100% confidence? What box did she choose (A to E) first?

you can safely assume that the smelling skill portion was untrue.

I think I would...

choose the 3 dozen white balls (Box C).

Then

I would take note of the weight of the box

So when I

picked up the bag 1 to "sniff" it, I would determine if it was 3x lighter. If it is, then there are two boxes of 1 dozen white balls in the bags (Box A & B). If it's near the same weight or heavier, then there are boxes of yellow balls, 3 dozen and 6 dozen (Box D & E) in the two bags.

This should give a very high (100%) confidence level.