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99 Paul Erd\"o{}s, a famous mathematician you might have heard about, said |
99 Paul Erd\"o{}s, a famous mathematician you might have heard about, said |
100 about this conjecture: ``Mathematics may not [yet] be ready for such |
100 about this conjecture: ``Mathematics may not [yet] be ready for such |
101 problems.'' and also offered a \$500 cash prize for its solution. |
101 problems.'' and also offered a \$500 cash prize for its solution. |
102 Jeffrey Lagarias, another mathematician, claimed that based only on |
102 Jeffrey Lagarias, another mathematician, claimed that based only on |
103 known information about this problem, ``this is an extraordinarily |
103 known information about this problem, ``this is an extraordinarily |
104 difficult problem, completely out of reach of present day mathematics.'' |
104 difficult problem, completely out of reach of present-day mathematics.'' |
105 There is also a \href{https://xkcd.com/710/}{xkcd} cartoon about this |
105 There is also a \href{https://xkcd.com/710/}{xkcd} cartoon about this |
106 conjecture\here{https://xkcd.com/710/}). If you are able to solve this |
106 conjecture\here{https://xkcd.com/710/}). If you are able to solve this |
107 conjecture, you will definitely get famous.}\bigskip |
107 conjecture, you will definitely get famous.}\bigskip |
108 |
108 |
109 \noindent |
109 \noindent |
151 The \textit{last-odd} function will only be called with numbers that are not |
151 The \textit{last-odd} function will only be called with numbers that are not |
152 powers of 2 themselves.\hfill\mbox{[1 Mark]} |
152 powers of 2 themselves.\hfill\mbox{[1 Mark]} |
153 \end{itemize} |
153 \end{itemize} |
154 |
154 |
155 \noindent |
155 \noindent |
156 \textbf{Test Data:} Some test ranges and cases are: |
156 \textbf{Test Data:} Some test cases are: |
157 |
157 |
158 \begin{itemize} |
158 \begin{itemize} |
159 \item 1 to 10 where $9$ takes 19 steps |
159 \item 1 to 10 where $9$ takes 19 steps |
160 \item 1 to 100 where $97$ takes 118 steps, |
160 \item 1 to 100 where $97$ takes 118 steps, |
161 \item 1 to 1,000 where $871$ takes 178 steps, |
161 \item 1 to 1,000 where $871$ takes 178 steps, |