Exploring Quento

I found this game a few months ago, and since playing it, I have been thinking of a lot of questions that I think would be fun for students to explore. 

If you're unfamiliar, Quento is a math game that tests the user's ability to do basic arithmetic. As you can see from the image, there are varying levels of difficulty, and the objective of the game is to combine the numbers in such a way so as to get the desired number. The trick is that the user can only use the specified number of numbers to get the result.

I have had quite a bit of fun playing this game, and I was glad that I was able to show my students the game on the last day of this past school year. While playing it as much as I have, I have been thinking of some fun questions about the math around the game. 

Aside from the obvious arithmetic component, Quento has some interesting design questions too. 

Question 1:

How many rounds could the game have? 

I like this counting problem because it requires the distinction between having numbers repeating and not. 

Question 2: 

How long will it take before I reach the final round? 

Having played through over 300 rounds, I wonder if I'll ever reach the end of the game. 

Question 3:
How many positive (and negative solutions) are there for each section of a round?

The fun part of this question is finding multiple ways to get 5 (for example) using only two or three numbers. Also, while negative numbers can be used to get a result, there have not been any negative solutions in the entire game. What if there were? (I guess that's question 3b).

Question  4:
By how much does the difficulty increase as more numbers need to be used to get a solution?

This is interesting because, while Quento does not have a timer, difficult could be measured in how long it takes to reach a solution. It could also be measured in the number of possible arrangements that arrive at the solution, which is connected to question 3.

Question 5: 
Could there be a level that requires using six numbers?

Quento has a "Hard" setting that I have not yet tried, but it only goes up to requiring four and five numbers. Would a round of six fall into the "Easy" or "Hard" category? (5b)

What do you think? 
I encourage you to try out the game, and ask your own questions. My dad and I are having a competition to see who can get further in the game, and it is a nice game for keeping your arithmetic skills sharp. I also encourage you to show your students the game, and ask them what questions they have about it. It comes on many platforms for free, so let me know what you come up with.