Your second sentence is too hard to do!

Number Theory Level 1

The above is a sudoku puzzle. Fill up all the missing cells. Submit your answer as the product of all the $9\times9=81$ numbers in this puzzle.

Notation: $!$ is the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .

Image Credit: The Telegraph .

(9!)^8

(9!)^7

(9!)^9

(9!)^{10}

1 solution

Zach Abueg
Jan 17, 2017

The numbers in one $3 \times 3$ grid are always $1, 2, 3, 4, 5, 6, 7, 8, 9,$ so their product is $9 \times 8 \times 7$ $\times$ $...$ $\times$ $3 \times 2 \times 1,$ or $9!$

Since there are nine $3 \times 3$ grids, all of which consist of the same numbers $1$ through $9$ , the product of all of the numbers in a sudoku puzzle equals the product of numbers in one $3 \times 3$ grid, multiplied by itself $9$ times, or simply

$(9!)^9$

But but but... The question requested us to fill up all the missing cells first.

Can you show us that the sudoku yields a (or at least one) solution?

Pi Han Goh - 4 years, 5 months ago

This is the most known sudoku years ago. Since there is no human approach, it is done by the computer/program.

I wish that someone can provide the deduction with the known technique besides guessing and Nishio .

Otherwise, here is the spoiler to solve the sudoku.

Michael Huang - 4 years, 4 months ago

Your second sentence is too hard to do!

Image Credit: The Telegraph .

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