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Puzzles on square grids

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Sudoku puzzles are incredibly popular with mathematicians and non-mathematicians alike. However once you have solved a few of them, or even written a program to solve them for you, then can become tedious.
But this does not mean an end to writing digits in boxes: as this blog post will reveal, there are a great number of other puzzles which revolve around arranging digits correctly.

3×3 Grids

The aim of all the puzzles in this section is to place the digits 1 to 9 in the boxes in order to make certain types of number in each row and column.

Puzzle #1

even
prime
cube
prime cube prime
In this first puzzle, place the digits 1 to 9 in the boxes so that the three digit numbers in the first, second and third rows are even, prime and cube respectively and the three digit numbers in the first, second and third columns are prime, cube and prime respectively.

Of course many more puzzles of this type can be created. Here are a few I have designed:

Puzzle #2

emirp*
even
emirp*
emirp* odd square

*An emirp number is a prime number which is a different prime number when the digits are reversed.

Puzzle #3

multiple of 17
multiple of 25
multiple of 9
multiple of 11 multiple of 16 multiple of 12

Puzzle #4

prime
prime
prime
prime square prime

2×2 Grids

Of course, there is no need to restrict this type of puzzle to 3×3 grids. Here are some puzzles on 2×2 grids:

Puzzle #5

prime
multiple of 8
prime multiple of 4
Can you place the digits 1, 2, 3 and 4 in this grid so that all the two digit numbers formed have the required properties?

Puzzle #6

prime
prime
prime prime
Can you place the digits 1, 3, 5 and 7 in this grid so that all the two digit numbers formed are prime?

Puzzle #7

prime
prime
prime prime
Can you place four different digits from 1 to 9 in this grid so that all the two digit numbers formed are prime? How many ways can this be done?

And Finally…

Similar puzzles can be formed from non-square grids, like these:

Puzzle #8

prime
prime
prime prime prime
Can you place the digits 1, 3, 5, 7 and 9 in this grid so that all the numbers formed are prime?

Puzzle #9

prime
prime
prime prime prime prime
Can you place the digits 1 to 7 in this grid so that all the numbers formed are prime?

The answers to the puzzles in this post will be appear here from Sunday 19th July at midday. If you have enjoyed these puzzles, why not try putting some more digits in boxes in our £100 prize crossnumber.

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Matthew Scroggs is a PhD student at UCL working on finite and boundary element methods. His website, mscroggs.co.uk, is full of maths and now features a video of him completing a level of Pac-Man optimally.
Twitter  @mscroggs    Website  mscroggs.co.uk    + More articles by Matthew

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