# Ten Crypto Problems Assignment

## Abstract

This assignment is intended to afford an opportunity to consider the Crypto problem. Ten problems, posed in the assignment, are considered for solution. The solutions are presented in CSL, the prescribed way to express solutions to Crypto problems. A bit of analysis of the solutions is performed. I present a few thoughts on how I think I go about solving Crypto problems. I translate one of the solutions into English.

## Ten Crypto Problem/Solution Pairs

1. Can you make 2 from ( 3 7 8 5 8 )?
2. ( ( (8 - 8) * 7)+(5 - 3) )

3. Can you make 5 from ( 15 11 2 4 15 )?
4. ( ( (15 - 4) - (15 - 11) ) - 2 )

5. Can you make 1 from ( 12 14 11 12 5 )?
6. ( (5 - (14 - 11) ) - (12 / 12) )

7. Can you make 13 from ( 12 4 10 15 5 )?
8. ( ( (12 / 4) + (15 - 10) ) + 5)

9. Can you make 15 from ( 5 1 1 10 11 )?
10. ( ( (10 - 5) - 1 ) + (11 * 1) )

11. Can you make 0 from ( 7 11 4 13 3 )?
12. ( (7 - (4 + 3) ) * (11 + 4) )

13. Can you make 8 from ( 12 4 2 2 1 )?
14. (12 / 4) + (2) + (2) + (1)

15. Can you make 1 from ( 9 11 14 2 13 )?
16. ( ( (14 - 9) - (13 - 11) ) - 2)

17. Can you make 3 from ( 0 9 0 9 7 )?
18. It is not possible to make 3 using the four operators given in this problem setting. It would require an exponent operator which was not among the four operators asked of us.

19. Can you make 13 from ( 1 6 12 1 8 )?
20. ( (12) + ( (6 + 1 + 1) / 8 ) )

## Analysis / Description / Translation Exercises

1. Which two of your solutions do you believe to be most similar? Why?
2. I believe my solutions for problems 2 and 8 were the most similar. This is because they both only required one type of operator in order to solve the cryto problem.

3. Which one of your solutions do you believe to be most different from all the rest. Why?
4. I believe question number 9 had the most different solution because I was unable to find a fully parenthesized arithmetic expression.

5. Which one of the problems do you think took the longest for you to solve?
6. I know problem number four took the longest because for each problem I wrote on paper first then rewrote it on my website. For question four there were more lead marks on my paper and a lot of erasing before it led me to my final answer.

7. Translate your solution to problem Number 7 to English -- striving to do so in an appropriately expressive way -- artfully and unambigously.
8. Twelve divided by four plus two plus two plus one.

9. In one relatively short paragraph, articulate how you think you go about solving a Crypto problem.
10. Usually for a Crypto problem I like to write the goal (which is what we are trying to make) on paper along with the numbers given to me in the problem set. I then use mental math in my head usually starting with addition and subtraction operators and trying to obtain the goal. If these two operators are not enough I will move on to the division and multiplication operators. I then add on the parentheses when needed, in order to create a fully parenthesized arithmetic expression.