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**kumark23****Member**- Registered: 2021-08-11
- Posts: 1

Fill the white boxes such that each equation is satisfied

*Last edited by kumark23 (2021-08-11 06:57:09)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,750

Hi kumark23, and welcome to the forum;

This type of puzzle usually lists the numbers that you have to choose from to fill the blank squares, and each number can only be used once.

Those numbers are often 1 to 9, and this group solves your puzzle.

Hint: The top row can only contain a particular group of three numbers that sum to 24.

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,635

The down totals add to 14 + 11 + 20 = 45 = ∑ n up to 9. This does suggest that you're meant to use the numbers 1 to 9, once only.

There are two big clues. the top three must add to 24 and Killer Sudoku fans will know that can only be achieved in one way. The other is the bottom row. We know it's 4 + ? + ? = 10 and there's only one pair of numbers that will fit that.

So it shouldn't take long to figure out those and then the rest will fall into place.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,750

Hi Bob;

Bob wrote:

The down totals add to 14 + 11 + 20 = 45 = ∑ n up to 9. This does suggest that you're meant to use the numbers 1 to 9, once only.Bob

Yes, I think so, since all down operators are '+'.

Just for interest, the following, with a somewhat different scenario (although the down totals also sum to 45, like the OP's), is from a puzzle book I have:

However, not all down operators are '+', and the numbers used are 2 to 9, once only, except for 2 (twice)...which is why '∑ n up to 9' can't be applied to mine.

*Last edited by phrontister (2021-08-13 14:26:16)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 9,635

hi kumark23

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,750

Hi Bob,

Just playing with Excel's Solver (not that kumark23's puzzle needs that sort of help), and it found your solution.

There's also another solution (the one I found manually just before my first post) that the Solver doesn't find without me first entering something somewhere on the grid...and I stumbled across several options of what to put where to extract that solution.

One Solver shortcoming is that it stops computing at the first solution it finds, but sometimes I've managed to get more than just the one result by influencing Solver's computation process somehow...eg, as per the above.

*Last edited by phrontister (2021-08-14 15:29:11)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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