Problem 3075. Matrix of Multiplication Facts

Created by James

Solve Later

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This is James's daughter again, sneaking into his Cody account. Thanks to your help in my math class last year, I did great! But now they're giving me even harder problems. This time, they're giving me a 2x2 matrix of numbers, and asking me to make it a 3x3 matrix so the center numbers on each side multiply to the numbers in the corner. It's kinda hard to explain, so I'll just give you the example our teacher gave us in class.The matrix we were given is:<pre> 21 6
 35 10</pre>The correct answer is:<pre> 21 3 6
 7 0 2
 35 5 10</pre><ul><li>The two numbers touching the 21 are 7 and 3, and 7x3=21.</li><li>The two numbers touching the 35 are 7 and 5, and 7x5=35.</li><li>The two numbers touching the 6 are 2 and 3, and 2x3=6.</li><li>The two numbers touching the 10 are 2 and 5, and 2x5=10.</li></ul>The zero in the middle doesn't really matter, so I don't care what number you put in there. Some of the problems might have more than one answer, but as long as the numbers multiply out correctly, it's a good answer. All of the numbers have to be integers, though. Thanks again for your help!

This is James's daughter again, sneaking into his Cody account.  Thanks to your help in my math class last year, I did great!  But now they're giving me even harder problems.  This time, they're giving me a 2x2 matrix of numbers, and asking me to make it a 3x3 matrix so the center numbers on each side multiply to the numbers in the corner.  It's kinda hard to explain, so I'll just give you the example our teacher gave us in class.

The matrix we were given is:

21   6
 35  10

The correct answer is:

21  3   6
  7  0   2
 35  5  10

* The two numbers touching the 21 are 7 and 3, and 7x3=21.
* The two numbers touching the 35 are 7 and 5, and 7x5=35.
* The two numbers touching the 6 are 2 and 3, and 2x3=6.
* The two numbers touching the 10 are 2 and 5, and 2x5=10.

The zero in the middle doesn't really matter, so I don't care what number you put in there.  Some of the problems might have more than one answer, but as long as the numbers multiply out correctly, it's a good answer.  All of the numbers have to be integers, though.  Thanks again for your help!

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Solution Stats

355 Solutions
63 Solvers

Last Solution submitted on Jan 09, 2022

Last 200 Solutions

Problem Comments

3 Comments

3 Comments

Andrew Dobrovolc on 11 Aug 2017

I think the test suite is broken, I appear to only get x = [21,6;35,10] as the input and y is being displayed as a vector instead of the matrix that is returned. So either the return is being compared to an x that was not sent or y being a vector is causing the test cases to always fail.

James on 22 Nov 2017

Andrew, I just tried resubmitting my original solution, and the test suite was OK. What is the exact problem that you're having with the test suite when you submit your solution?

Riccardo Dessì on 8 Mar 2018

nice one!!

Solution Comments

Solution 1215290

1 Comment

1 Comment

Daigo on 9 Jan 2022 at 17:26

I have no idea what the leading solution (Solution 1215290) is doing in the last line...

Solution 595053

2 Comments

2 Comments

Tim on 11 Mar 2015

Test suite compares y to itself--should compare y to x.

James on 12 Mar 2015

Hah! Great catch. It's fixed now, but you still get a like for being so sneaky...

Problem Recent Solvers63

Problem Tags

elementary_school_math factors matrix

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