Quick and simple ClassPad programs for solving problems such as those posed by Project Euler.

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1 Quick and simple ClassPad programs for solving problems such as those posed by Project Euler. Some readers may be familiar with Project Euler ( It is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems. The intended audience include students for whom the basic curriculum is not feeding their hunger to learn, adults whose background was not primarily mathematics but had an interest in things mathematical, and professionals who want to keep their problem solving and mathematics on the edge. The problems range in difficulty and for many the experience is inductive chain learning. That is, by solving one problem it will expose you to a new concept that allows you to undertake a previously inaccessible problem. So the determined participant will slowly but surely work his/her way through every problem. Problem 1 from Project Euler: If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below We'll use this problem to explore the Program application on ClassPad. Open the Program application. Tap Edit, New File. Enter a name for the program, such as pe1 and tap OK. The program editor opens and on the third row the program name is displayed. We're ready to create our program. Before we start our program here is a brief review of the modulus function. The modulus function returns the remainder when a is divided by b. On ClassPad use mod(a,b). Inspection of the screen shown here reveals that when mod(a,b) is zero, then a is a multiple of b.

2 Here's a possible program to tackle Problem 1 for natural numbers below 10: What do these lines of code do? Notes Find commands using the Ctrl, I/O and Misc menus or simply type in code using the abc keyboard. Pay attention to upper and lower case - programming languages are usually quite strict. Start a new line by pressing the EXE key. Blank lines are also ignored by ClassPad, as are spaces at the start of a line. This is useful to indent lines of code, and so make the program structure clearer. Spaces are critical around commands such as Local, For... and If... and are likely sources of syntax errors. Use the ClassPad user manual (free online from if you need help. 'v124/09/2012 Local i,t 0 t For 1 i To 9 Lines starting with an apostrophe are ignored and so you can use them to add comments to your program, such as version and date written, etc. Local variables are used only within program and then deleted. You can skip this line, but it's a good way to keep your ClassPad, and those of others who use your program, tidy. Store the value 0 in the variable t - we will use t to keep a running total of the sum of the multiples of 3 and 5. For is the start of a loop, in which the counter i is increased from 1 to 9 (in steps of 1). Spacing is critical for this line, with just ONE space after For and either side of To. If mod(i,3)=0 Or mod(i,5)=0 If either of these conditions are true, then we have either a multiple of 3 or a multiple of 5. In this case, ClassPad will carry out the code between Then and IfEnd lines. Otherwise the program will jump to the code after the IfEnd line. Watch your spacing again here to avoid syntax errors. Then Then always follows an If statement. t+i t Add the value of i to the total t and then assign this value back to t. IfEnd IfEnd is the last line of our If <this is true> Then <do this> IfEnd construct. Next Next tells the program to loop back to the For line and increase i by 1. ClrText Print t ClrText clears the result screen. Print writes the value of t to the result screen.

3 Running the program Once your code has been entered, tap Edit, Save File and then tap. Check that the name of the current program is pe1 and tap. If all goes well, the Status box appears with the message 'Done' and you can tap OK. If all goes well, the result window should display the total as 23. Tap to return to the program application. Errors If any error messages appear, either when saving the program or running the program, ClassPad usually opens the program in the editor and places the cursor where it considers the error to be. Unfortunately, this is often not the location of the error, so you will need to check your typing carefully, paying attention to upper and lower case, spaces, and so on.

4 Modify the program to accept a parameter Tap Edit, Open Editor to edit your program. Now that we have checked the program works for small values, we can modify the program to find the sum of all the multiples of 3 or 5 below Insert n in box under scissors icon, add n to Local variables and change 9 to n in For statement. Save File and tap. Enter 999 in Parameter box (value for n) and tap. About 20 seconds later, the program returns the sum. Modify the program to display progress Open the program editor again. When a program takes a long time to produce a result, we can display interim values to add some user interest. The program will take longer to run, but doesn't seem to because of the distraction. The Locate column, row, value command will display a value at a specific position on the screen. Make other changes (delete Print and move ClrText), save changes and run again. Try running the program in main as shown below. ClassPad programming help on the web (Lessons 15 and 16) (Advanced tab, Lesson 985)

5 Additional programming tips - Ctrl and I/O Menus If... Then... Else... IfEnd Use for branching and decision making. Program takes two values and prints out the difference. Else is optional. Can also include ElseIf statement. For... Next Use for repeating fixed number of times Program sums the squares of all integers from 1 to n. Can add 'Step k' to increment i in steps of k. Do... LpWhile Use for looping until a condition is met. Programs finds the smallest number which has a square greater than n. Beware of writing an endless loop! Press the Clear button to break out of such a program. While... WhileEnd Use for looping, but checks for condition at start of loop. Program sums the roots of integers from 1 to n. Again, beware of endless loops. Input Use for obtaining a single number input from user. Program displays all factors of any integer. Note use of colons to enter multiple commands on a single line. Locate Use for writing to specific location (x,y) on the result screen. This program prints the squares of numbers from 1 to n at the location (1, 20) on the screen. Upper left corner is (1,1). x: 1 to 290 y: 1 to 290

6 Further problems to program The sum of 48 and 1 is a perfect square = 49 and 7 7 = 49 The sum of one-half of 48 and 1 is also a perfect square = 25 and 5 5 = 25 What is the next integer n greater than 48 for which both n + 1 and n are both square numbers? Soln: The next integers are 1680, and Take the number 2025 Split down the middle into two 2-digit numbers 20 and 25 Sum these two numbers = 45 Square this result 452 = 2025 The result is the same as the number we started with. Is there another 4-digit number with this property? Soln: Both 3025 and 9801 have this property The integer 36 is both a square number and a triangular number: 62 = 36 and = 36 How many other integers less than exist that are both square and triangular numbers? Soln: There are 7 such integers with this property: 1, 36, 1 225, , , and One is the smallest positive integer that is a perfect square, cube, and fifth power. That is 1 = = = 1 5 What is the next smallest integer with this same unique property? Soln: The next integer is