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LostInParadise's avatar

Care to see a simple but surprising math trick?

Asked by LostInParadise (32216points) July 30th, 2023

After I came across this, I knew I had to share it here.
Create a small rectangular array of numbers where each row increases from left to right but is otherwise randomly organized. Now order each column from top to bottom. Surprise! The rows are still ordered from left to right.

The book I found this in gave what it considered an explanation, but which I could not make sense of.

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2 Answers

LuckyGuy's avatar

I woke up this morning, sat down to eat breakfast, saw your post and thought “Oooo! A simple math trick. Fun!”
I’m sitting here with my coffee but I don’t get it.

I tried:
2.3.6
1,8,9
3,4.5
What am I missing? Aren’t the rows always ordered from left to right? That is how they were set up. Clearly I’m doing something wrong.

LostInParadise's avatar

I must not have been clear on how to do this. For example, I should have specified that all the numbers are distinct. In your example, replace the final row 3.4.5 with 4.5.7. We have
2.3.6
1.8.9
4.5.7

Now order all the columns from top to bottom
1.3.6
2.5.7
4.8.9

The rows are all different, but they still increase from left to right.

Here is another example
5.10.15
7.11.14
3.12.13

3.10.13
5.11.14
7.12.15

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