Can you complete this magic square?

Logic Level 4

The $4\times 4$ square above is a magic square, where the sum of every row, column, or diagonal is equal, and the letters $A$ to $N$ denote the distinct 2-digit prime numbers apart from 49 and 7 given.

If all the numbers are rearranged into the matrix $P$ on the right as shown, what is the determinant of matrix $P$ ?

The answer is 0.

1 solution

Worranat Pakornrat
Dec 22, 2015

The numbers in the magic square are shown above with equal sum of 180 in every row, column, or diagonal. When we compute the determinant of the matrix P, it will equal to 0.

How do you construct this matrix?

Pi Han Goh - 5 years, 5 months ago

Honestly I came across it by chance. I didn't know it would have determinant=0. I was a little surprised myself.

Worranat Pakornrat - 5 years, 5 months ago

Is this solvable by hand?

Pi Han Goh - 5 years, 5 months ago

@Pi Han Goh – I did solve it by trial & error. I'm not sure if the Siamese method would work in this case as they are primes, but surely with prime restriction under 100, it's solvable by hand.

Worranat Pakornrat - 5 years, 5 months ago

@Worranat Pakornrat – The Siamese method does not work however for n-even squares .

Trial and error? So it's still solvable by hand? I highly doubt that. Can you show us how you've approach it? Thanks.

Pi Han Goh - 5 years, 5 months ago

@Pi Han Goh – I just wrote a more thorough approach and square construction in my new question "Almost Primes Square":

https://brilliant.org/problems/almost-primes-square/?group=DUXfJCTmX8dy&ref_id=1065663

This time, only 49 is composite and other numbers are 2-digit primes. Hope it'll be clear. ;)

Worranat Pakornrat - 5 years, 5 months ago

@Worranat Pakornrat – Well, the first question is how do you get 180?

Tran Hieu - 5 years, 5 months ago

Can you complete this magic square?

The answer is 0.

1 solution

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