David Hilbert was a famous mathematician and philosopher (1862-1943). Because he was so famous, in 1900, at the second International Congress of Mathematicians in Paris, he gave a speech in which he proposed 23 problems in different fields of mathematical research. Mathematicians all over the world have worked hard to discover the answer to Hilbert's problems and in the process have discovered new branches of mathematics. Not all of them have been solved.
These are a similar (but significantly more easy) list of problems. It is your job to solve two of them. (Yes, you can solve more. Yes, that will result in more marks.) We are going to use the brute force programming approach to solve all of the them. The computer can do repetitive questions easily, so let's use it to do so.
Solving a simpler problem - You don't need to use a chart for this and you may wish to hand write it. Make sure that all of the required information is included. Please keep all of the information for one problem together.
| Simpler Problem | Information Required | Solution (Show work) | Comments - especially about whether or not this would be hard to code. |
| 1. How many Mondays fell on the first of the Month in 1900 and 1901? | (This one is finished for you) 1 Jan 1900 was a Monday. Sept, April, June, Nov have 30 days. All rest have 31 except Feb. which has 28. A leap year occurs on any year divisible by 4, but not on a century year unless it is divisible by 400. |
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| 2.Find the sum of the digits in 10! | What is factorial? | ||
| 3. What is the 7th prime number? | What is a prime number? | ||
| 4. What is the smallest number that can be divided by all of the numbers between 1 and 5? | How can you use % to determine if a number is divisible by 2? | ||
| 5. What is the sum of the first four triangle numbers? | What is a triangle number? | ||
| 6. If all the numbers from 98 to 102 were written out in words, how many letters would be used? | What are the conventions for using 'and' in numbers? What are the rules for writing out numbers in words? |
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| 7. Find the sum of the odd numbered terms of the fibonacci sequence whose value is less than 40. | What is the fibonacci sequence? How do you make terms in the fibonacci sequence? Which are the odd numbered terms? |
Conclusion
A short paragraph (point form is even better) outlining which TWO you will solve. Do not write that you will solve them all. I want you to pick two.
Analysis Rubric (4 Levels)
| 0-2 | 3 | 4 | |
| Analysis | Less than 5 solutions right. More "information required" needs to be filled in. | 5 to 6 Solutions right. Most "information required" is filled in. | All right. Well filled in. |
| Formatting | Title. White Space. | Explains final choices. | Easy to follow. Subtitles. |
For the two problems that you picked, code the part that is asked for.
| Problem | Design Code (What you need to do for design) |
1. How many Mondays will fall on the first of the month in the 21st century? |
Given a year entered by the user, determine if it is a leap year. |
2. Find the sum of the digits in 100! |
What is the sum of digits in a number that the user enters? |
3. What is the 50th prime number? |
Given a number entered by the user, is it prime? |
4. What is the smallest number that can be divided by all of the numbers between 1 and 15? |
What are all of the factors of a number that the user enters? (Positive only) |
5. What is the sum of the first 50 triangle numbers? |
If a user enters a number, what is its triangle number? |
6. If all the numbers from 1 to 500 were written out in words, how many letters would be used? |
Given a number entered by the user, print out the words for it. |
7. Find the sum of the odd numbered terms in the fibonacci sequence whose value is less than 1 million. |
When a user enters a number, print out that term of the fibonacci sequence. |
Design Rubric (4 Levels)
| 0-2 | 3 | 4 | |
| Design Code | 2 Sub Problems Coded, may be errors. | 2 Sub Problems Coded. Working well. | 3 Coded. Working perfectly. |
| Formatting | Did a monkey type this? | Title. White Space. | Easy to follow. Subtitles. |
| 0-2 | 3-4 | 5-6 | 7 | 8 | |
| Problems Solved Correctly | None, but an attempt | 1 correct. | 2 correct. | 3 correct. | More than 3 correct. |
| Code Used. | Some attempt at a menu and code. | A Menu to choose options. | Nested loops and ifs to solve problems. | Something new: Switch, do/while, for or ? used. | Lots of new or efficient code used. Something creative added. |
| Comments | Title comments. | A Few. | Before ifs and loops. | At the top of the code for sources of new things. | Sourcing used MLA format for new things. |