University of North Dakota Palindromic Number Questions

Directions:

• Do not use string indexing, lists, list indexing, or recursion in this unit. You should not use strings at all in fact except where they are explicitly required in some spicy problems.
• Do not hardcode the test cases in your solutions.

Problems:

1. isPalindromicNumber(n) [10 pts]
   Write the function isPalindromicNumber(n) that takes a non-negative int n and returns True if that number is palindromic and False otherwise, where a palindromic number is the same forwards as backwards. For example, these numbers are palindromic: 0, 1, 99, 12321, 123321, and these numbers are not: 1211, 112, 10010.
2. nthPalindromicPrime(n) [10 pts]
   Write the function nthPalindromicPrime(n). See here for details. So nthPalindromicPrime(0) returns 2, and nthPalindromicPrime(10) returns 313.
3. hasConsecutiveDigits(n) [10 pts]
   Write the function hasConsecutiveDigits(n) that takes a possibly-negative int n and returns True if somewhere in n some digit occurs consecutively (so the same digit occurs twice in a row), and False otherwise. For example, these numbers have consecutive digits: 11, -543661, 1200, -1200, and these numbers do not: 1, 123, 12321, -12321.
4. carrylessAdd(x, y) [35 pts]
   First, you may wish to read the first page (page 44) from here about Carryless Arithmetic. Or, just understand that carryless addition is what it sounds like — regular addition, only with the carry from each column ignored. So, for example, if we carryless-ly add 8+7, we get 5 (ignore the carry). And if we add 18+27, we get 35 (still ignore the carry). With this in mind, write the function carrylessAdd(x, y) that takes two non-negative integers x and y and returns their carryless sum. As the paper demonstrates, carrylessAdd(785, 376) returns 51.
5. longestDigitRun(n) [35 pts]
   Write the function longestDigitRun(n) that takes a possibly-negative int value n and returns the digit that has the longest consecutive run, or the smallest such digit if there is a tie. So, longestDigitRun(117773732) returns 7 (because there is a run of 3 consecutive 7’s), as does longestDigitRun(-677886).

6. spicy: play112 (The 112 Game) [65 pts]
See “The 112 Game” here (skip to Part B). Be sure to follow the spec exactly, so the autograder can properly grade your work! Also, note that the test function in that writeup uses Python 2, but the one in the hw2.py file we provided uses Python 3.