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The Largest Total is a puzzle in Professor Layton and the Curious Village.

Puzzle

Nine squares are carved into a piece of wood.

US Version

Arrange nine unique numbers between one and 51 so that any three numbers have the same sum when added vertically, horizontally, or diagonally.

While several combinations are possible, your task is to find the number that occupies the center square when you arrange the numbers to yield the highest possible total.

UK Version

Arrange nine unique numbers between one and 51 so that every vertical, horizontal and diagonal line of numbers crossing through the middle square has the same sum.

Arrange the numbers so that they yield the highest possible sum.

What number occupies the middle square?

Hints




Click a Tab to reveal the Hint.

There are 51 numbers you can choose from, but since you're trying to get the largest total possible, you might want to try the bigger numbers first.

As stated in Hint One, you should place large numbers in your square.

Use the numbers 43 through 51 when formulating your answer.

It might not seem obvious at first, but the center number is used in every single tabulation. Since you're trying to get the largest sums possible, doesn't it make sense to put the largest number right in the middle?


Solution

Incorrect

Give it another shot!

Are you sure that you've found the number that gives you the largest total when added vertically, horizontally, and diagonally?

What should your total be?

Correct

Great job!

To get the largest total possible from any three vertical, horizontal, or diagonal numbers, you should place the largest number available in the middle square.

Once you've decided on that as your middle number, all you need to do is test whether you can complete the square.

The full solution should look something like the diagram above.

CV116S

A big thanks to http://professorlaytonwalkthrough.blogspot.com

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