**Hunting Submarines**

##### (John Costas, 1965)

Costas arrays were part of submarine warfare and a great way to get practice with slopes. It is an unsolved problem of mathematics whether a Costas array exists for all nxn squares. The smallest square for which no answer is currently known is 32×32.

Here is the puzzle-sheet.

You don’t have to be a mathematician to have a feel for numbers.

**Standards for ****Mathematical Practice**

MathPickle puzzle and game designs engage a wide spectrum of student abilities while targeting the following Standards for Mathematical Practice:

##### MP1 Toughen up!

This is problem solving where our students develop grit and resiliency in the face of nasty, thorny problems. It is the most sought after skill for our students.

##### MP3 Work together!

This is collaborative problem solving in which students discuss their strategies to solve a problem and identify missteps in a failed solution. MathPickle recommends pairing up students for all its puzzles.

##### MP6 Be precise!

This is where our students learn to communicate using precise terminology. MathPickle encourages students not only to use the precise terms of others, but to invent and rigorously define their own terms.

##### MP7 Be observant!

One of the things that the human brain does very well is identify pattern. We sometimes do this too well and identify patterns that don't really exist.