**Using Least 1s**

##### (Conway & Guy, 1962)

Using multiplication and addition try to create the target number using the least number of ones. For example… to get to the number 12, you could do (1+1+1+1)*(1+1+1) or (1+1+1+1+1)*(1+1)+1+1 but the first solution is better since it uses only seven ones. This is good for elementary school.

Now we’ll try it using addition and exponents, but not multiplication. Which pair of operators is fastest? This is good for older students.

We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.

**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.