Real MATHEMATICS – Game #7

Judge Seesaw

There are 12 gift boxes on the table. They all have identical sizes and gift wraps.

rectangular white and red gift box

11 of them weight the same as the 12th box weights different from others.

Goal: Finding the oddly-weighted box.

Prize: 50 million old Turkish liras worth Oreo. (Because Oreo is the most beautiful thing in life.)

Tools: You can use a seesaw to compare the weights of the boxes.

istockphoto-684156036-612x612

Challenge: You will have to guess the oddly-weighted box in at most 3 tries.

Judge Seesaw 1.0.1

It is the most basic version of the game where it is known if the 12th box is heavier or lighter than other 11 boxes.

At this point give yourself a few minutes and think on a solution when it is known that the 12th box is heavier than the rest.

***

Time is up. Here is the solution:

I assumed that the 12th box is heavier than the rest of the boxes. Then we should divide 12 boxes into three groups of 4.

In the first try we will take any two of those groups of 4 and place them on the ends of the seesaw. There will be exactly two possible outcomes:

Situation A: Seesaw is balanced.

tahte

Two groups have equal weights which would mean the oddly-weighted box must be among the third group of 4.

 

In the second try we will take the third group of 4, divide those two-by-two and place them on the ends of the seesaw.

tahte3

We will be seeing that the seesaw is tilted to one side. That happens because heavy box sits on the seesaw.

 

In the third try we’ll be taking the heavier couple from previous measure and place them one-by-one on the ends of the seesaw.

tahte4

The seesaw will be tilted in favor of the heavier box. Hence we found the oddly-weighted box in exactly three tries.

 

Situation B: Seesaw is tilted.

tahte2

 

This happens because oddly-weighted box is among one of the groups of 4 boxes. Take that group and apply the same methods we did in situation A.

One wonders…

Judge Seesaw 2.0.1

In this version of the game we have no idea whether the 12th box is heavier or lighter than the rest of the boxes.

Even though it seems like a slight change, this game has become much harder compared to the version 1.0.1.

This is why I will give you a little time. I’ll include the answer in the next post.

M. Serkan Kalaycıoğlu

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