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LEARN TO GUESS GUESS TO LEARN (C) 1988 D. Bodnar The Learn to Guess series is a set of four programs that are designed to develop problem solving strategies and reinforce whole number concepts. Each of the programs is complete in itself and uses the computer's secretly chosen number as a means to challenge student's mathematical and analytical abilities at a range of difficulty levels. The series is composed of the following programs: GUESSME GUESSME, for from one to four players, is designed to help students in grades 1-8 to develop problem solving strategies while trying to guess the computer's secret number. It also serves as an introduction to the concepts and procedures used in the other programs in the series. Depending on the difficulty level, the numbers chosen by the computer may be positive and/or negative. ROMAN GUESSME This program is identical to GUESSME, except that all of the numbers used in the game are displayed as, and must be entered as, roman numerals. ROMAN GUESSME is appropriate for students of all ages. NEAREST At first glance NEAREST, a game for from two to four players, seems to be a simple number guessing game, but it has a diabolical twist. Rather than telling if a guess is too high or too low, the computer uses a high resolution display to indicate which of the guesses that was made is CLOSEST to the computer's secret number. This program is appropriate for grades 2-8. SUPERGUESS SUPERGUESS, for two to four players, is a program designed to help students in grades 3-12 to develop problem solving strategies in this most challenging number guessing game. Students must call upon all of their knowledge of prime numbers, composite numbers, factors, multiples, sums, differences and products as they compete against one another in a race across the computer's screen. The series requires an IBM-PC or compatible with 256K and a CGA or EGA display monitor and one disk drive. GUESS is distributed under the SHAREWARE concept. This simply means that I have given you the right to use this software, evaluate it and share it with your friends. All that I ask in return is that you register the program with me by sending a check for $15.00 to: David G. Bodnar 26 Ralston Place Pittsburgh, PA 15216 In return you will receive the latest version of the program, a complete, printed manual, an additional program, MATHDUEL, and a catalog of other educational software. LEARN TO GUESS (c) 1988 D. Bodnar Table of Contents GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 GUESSME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 GUESSME - Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . 2 GUESSME - Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . 4 ROMAN GUESSME . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 NEAREST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 NEAREST - Part 1 . . . . . . . . . . . . . . . . . . . . . . . . . 6 NEAREST - Part 2 . . . . . . . . . . . . . . . . . . . . . . . . . 7 SUPERGUESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 OBJECTIVES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 SUPERGUESS - Part 1 . . . . . . . . . . . . . . . . . . . . . . . 8 SUPERGUESS - Part 2 . . . . . . . . . . . . . . . . . . . . . . . 11 LEARN TO GUESS (c) 1988 D. Bodnar GETTING STARTED Boot the computer as you normally would. Once the A> prompt is displayed on the screen type GUESS and press the ENTER/RETURN key. The program selection menu will appear. It looks like this: 1. GUESSME ON THE NUMBER LINE (1-4 players) 2. ROMAN GUESSME ON A NUMBER LINE (1-4 players) 3. NEAREST NUMBER (2-4 players) 4. SUPER GUESS!!!!! (2-4 players) 5. end You may choose one of the five options by pressing the number to its left or by typing its initial letter. For example, you may choose GUESSME by pressing 1 or G. Next you must type in the player information that is needed for each game. The number of players is one to four for GUESSME and ROMAN GUESSME and two to four for NEAREST and SUPERGUESS. A single player can use either of the last two games by entering two names and competing against himself/herself, perhaps while using two different strategies. After the number of players and their names are typed the difficulty level for each game must be chosen. A detailed description of each level is given in the section that describes each program. The following manual is tutorial in nature and assumes that you are running the programs as you read. 1 LEARN TO GUESS (c) 1988 D. Bodnar GUESSME GUESSME is a program designed to help students to develop problem solving strategies while trying to guess the computer's secret number. It also serves as an introduction to the concepts and procedures used in the other programs in the series. Student guesses serve to limit the range within which the computer's secret number is located. With practice, a strategy should evolve that will allow as student to rapidly and consistently discover the secret number. Once the number is discovered the student plays a 'Hangman' style game that challenges him to discover a number-word that the computer has chosen. OBJECTIVES The following objectives were used in the development of GUESSME: 1. Students will develop problem solving strategies that will allow them to systematically discover the computer's secret number. 2. Students will recognize a number line and the relationships of numbers on a number line. 3. Students will develop problem solving strategies that will allow them to discover the secret number-word that the computer has chosen. 4. Students will be able to work with negative numbers on a number line. GUESSME - Part 1 Once GUESSME has been chosen from the first menu and the number of students and their names have been entered, the difficulty level must be chosen. The difficulty levels determine the size of the number line and the range of numbers that will be used by the computer. The levels are as follows: Difficulty Level 1 -- numbers between 1 and 10 Difficulty Level 2 -- numbers between 1 and 100 Difficulty Level 3 -- numbers between 1 and 1000 Difficulty Level 4 -- numbers between 1 and 10,000 Difficulty Level 5 -- numbers between -5 and 5 Difficulty Level 6 -- numbers between -50 and 50 Difficulty Level 7 -- numbers between -500 and 500 Difficulty Level 8 -- numbers between -5000 and 5000 2 LEARN TO GUESS (c) 1988 D. Bodnar After the difficulty level is entered the playing field is displayed. Is consists of a number line displaying numbers in the range indicated by the difficulty level. The bar above the number line indicates that the computer's secret number could be anywhere on the number line. This bar will shrink as guesses are made. If two or more students are competing, one of their names will be chosen at random and he/she will be asked to make a guess. If a guess is out of the range that is indicated by the bar above the number line, a tone is sounded and the guess may be reentered. Once an acceptable guess has been entered one of three things will occur. First, if the guess is correct, a line will be drawn to the correct spot on the number line. If the guess is too large, the part of the bar above the number line to the right of the guess will be erased. Similarly, if the guess is too small, the part of the bar to the left of the guessed number will be erased. Guess-by-guess the bar above the number line will shrink until the correct number is chosen. If the number line is greater than 100 the screen will periodically 'zoom' in for a more detailed display. This 'zooming' will occur until the range of the number line does not exceed 100 units in size. If two or more students compete, their names are chosen at random. Occasionally the same student will have two consecutive turns, but each student will receive the same number of guesses. Once students have had an opportunity to play the game a few times they may wish to see how well they can do at guessing the number in the number of guesses indicated under # TO BEAT = at the top of the GUESS NUMBER box. This number is the most guesses it will take to guess a number if a pure 'binary' search strategy is used. A binary search always guesses the exact middle number in the range of possibilities. For 100 numbers the # TO BEAT is 7 guesses, for 1000 it is 10 and so on. In levels 1 and 2 the computer continually displays the range of acceptable guesses above the guesser's name. If a student in level 3 or above needs this type of help he/she may type H or HELP when asked to make a guess. 3 LEARN TO GUESS (c) 1988 D. Bodnar GUESSME - Part 2 The student who correctly guesses the secret number will be given the opportunity to win the game by guessing the second secret number, a number- word between 1 and 100. (In levels 1 and 6 the range is 1 to 10.) This number-word, such as SEVENTEEN or THIRTY-SIX, must be guessed letter-by-letter. The number of letters in the word will be indicated by a set of blanks across the center of the screen. To discover the word the student must choose a letter that he/she feels is included in the word. If the letter is in the word it will be inserted at the proper position. If the word contains more than one of the letter all of the occurrences will be displayed. Note that if the word contains a hyphen that it must also be guessed. An incorrect guess will end the student's turn at guessing the word and the game will continue with a second try at the number line. This routine continues until someone guesses the secret number-word in the second part of the game. The number line number changes each time the number line part of the game begins, but that the number-word remains the same until it is guessed. Once the game is completed an option of stopping or playing again is given. Answering Y to AGAIN(Y/N) will start the game from the beginning, using the same players and difficulty level. A response of N will return you to the first menu where a different game or set of players may be chosen. A player may quit the game and return to the main menu by typing the word END when asked for a guess. 4 LEARN TO GUESS (c) 1988 D. Bodnar ROMAN GUESSME This game is identical to GUESSME, except that all of the numbers on the number line are displayed as ROMAN NUMERALS. In addition guesses must also be entered as ROMAN NUMERALS. ROMAN SCREEN The difficulty levels are as follows: Difficulty Level 1 -- numbers between 1 and 10 Difficulty Level 2 -- numbers between 1 and 100 Difficulty Level 3 -- numbers between 1 and 1000 Difficulty Level 4 -- numbers between 1 and 2000 To select a number it must be entered as a ROMAN NUMERAL. That is, if you wish to guess 47 for your first guess, you must enter it as XLVII. An incorrect ROMAN NUMERAL will be ignored. With the exception of difficulty level 4 and the ROMAN NUMERALS, all facets of the game are identical to GUESSME. 5 LEARN TO GUESS (c) 1988 D. Bodnar NEAREST NEAREST is best when played by two or more different students compete. Again a secret number has been chosen by the computer. The student's guesses are compared to the secret number and to each other. The computer reports, not if a guess is too high or too low, but which of the guesses is closest to the secret number. This report is given in sentence form and on a graphic display. The difficulty levels for NEAREST are as follows: Difficulty Level 1 -- numbers between 1 and 10 Difficulty Level 2 -- numbers between 1 and 25 Difficulty Level 3 -- numbers between 1 and 50 Difficulty Level 4 -- numbers between 1 and 100 NEAREST - Part 1 The game screen shows the players' names, the current guess number and a number line whose size is determined by the difficulty level. One of the players will be chosen at random and a question mark will be displayed next to the name. Once that student's guess is entered another student will be chosen and so on until each has guessed. Each guess will be shown at the appropriate point on the number line as a dot. After all of the guesses are entered one or, in the case of a tie two, of the dots will be circled. If, for example, the guesses for a three player game were 18, 12 and 7 and the computer's secret number were 11, the dot over the 12 would be circled. If the secret number had been 15, both 12 and 18 would have been circled since they are an equal distance from 15. If a tie is indicated this can be a powerful clue that should allow the next player to win. The game continues in a similar fashion with each succeeding series of guesses being indicated higher and higher above the number line. An examination of the circled dots will help in finding the secret number. 6 LEARN TO GUESS (c) 1988 D. Bodnar NEAREST - Part 2 Once the secret number has been found, the second game screen will be displayed. Here the player who successfully guessed the secret number must accomplish a task similar to, but more difficult than, that used in GUESSME and ROMAN. A secret number-word, in the same range as that chosen under difficulty level, must be found. This time, however, no indication of the word's length is given. As a letter is guessed, it is placed on the screen if it is in the word. The correctly chosen letters are placed on the screen in the order in which they are guessed, not necessarily in the order in which they appear in the secret word. A player may continue guessing letters until an error is made or until all of the word's letters have been discovered. (Don't forget the hyphen!) Once all of the word's letters are on the screen, a box will be drawn around them to indicate that the guessing is complete. Now the player must determine what the screen number-word is. If, for example, the letters in the box on the screen were ITTLYSREEV-HN the correct guess would be 37. Notice that the final guess must be given as a numeral, 37, not as a word, THIRTY-SEVEN. 7 LEARN TO GUESS (c) 1988 D. Bodnar SUPERGUESS OBJECTIVES The following objectives were used in the development of SUPERGUESS: 1. Students will develop problem solving strategies that will allow them to choose among the clues that the computer has to offer. 2. Students will use their knowledge of the following concepts to help them to deduce the computer's secret number: A. Prime numbers have only two factors. B. Composite numbers have three or more factors. C. Zero and one are neither prime nor composite. D. A sum is found by adding numbers. E. A difference is found by subtracting numbers. F. A product is found by multiplying numbers. G. A number is even if it is evenly divisible by two. H. A number is odd if it is one more that an even number. I. Factors of a number are those numbers that divide evenly into the number. J. Multiples of a number are found by multiplying the number by 0, 1, 2, 3, 4, 5, ... and so on. 3. Students will develop problem solving strategies to help them to beat their opponent(s) in a race across the computer's screen. SUPERGUESS - Part 1 SUPERGUESS differs from the other games in this series in that the student buys clues to help him/her to discover the computer's secret number. It is also the only one of the games where each player may choose to work at a different difficulty level. This allows students of different ability or experience to compete. The difficulty levels are: Difficulty Level 1 -- numbers between 1 and 25 Difficulty Level 2 -- numbers between 1 and 75 Difficulty Level 3 -- numbers between 0 and 100 Difficulty Level 4 -- numbers between 0 and 150 The first game screen shows one of the player's names, his/her difficulty level and that he/she starts the game with 40 points. It also shows eight different clues that can be used to discover the secret number that the computer has chosen. 8 LEARN TO GUESS (c) 1988 D. Bodnar Each player may use his/her points to buy clues in their quest to discover the number. The number to the left of each clue is its 'cost' in points. (1) Prime/Composite (10) Digit Sum (10) Digit Difference (15) Digit Product (2) Number of Digits (1) Odd/Even (5) Number of Factors (2) Multiple of A clue is selected by pressing the UP and DOWN arrow keys until the marker is next to the clue that you wish to buy. Pressing ENTER will select the clue. The following is a brief description of what each clue means: *** Prime/Composite A number is prime if it has only 2 factors, 1 and itself. 7 and 13 are both prime numbers. If a number has more than 2 factors it is composite. 15 and 24 are composite numbers because they have many factors. 1 and 0 are neither prime nor composite. When this clue is chosen a P, C or N is displayed. *** Digit Sum To compute the digit sum the computer takes the digits that make up a number and adds them. The digit sum of 25 is 7 since +5=7. The digit sum of 148 is 13 since 1+4+8=13. *** Digit Difference The computer subtracts the smallest digit of a number from the largest. The digit difference for 84 is 4 since 8-4=4. The digit difference for 48 is also 4. The digit difference for a one digit number is the number itself. The digit difference for a three digit number is the difference between the largest and smallest digits. The digit difference for 138 is 7 since 8-1=7. *** Digit Product The computer multiplies all of the digits of the number to compute the digit product. The digit product of 17 is 7 since 1X7=7. The digit product of a one digit number is the number itself. 9 LEARN TO GUESS (c) 1988 D. Bodnar *** Number of Digits This is the number of digits that make up the number. The number of digits for 25 is 2, for 421 is 3. *** Odd/Even A number is even if it is evenly divisible by 2. A number is odd if it is one more than an even number. 3, 11, 83 and 133 are odd numbers. 4, 12, 5 and 130 are even numbers. *** Number of Factors This is the number of numbers that will divide evenly into the number. 12 has 6 factors. They are: 1, 2, 3, 4, 6 and 12. 50 has 6 factors. They are: 1, 2, 5, 10, 25 and 50. 17 has only 2 factors, 1 and 17, since it is a prime number. *** Multiple of? This clue allows you to choose a number and the computer will tell if the number that you choose divides into the secret number evenly. In other words, it tells if the secret number is a multiple of the number you select. If the number you pick is a factor of the secret number it is printed on the screen directly below Multiple of. If it is not a factor it is printed with an X. If the secret number were 24 and you picked 5 for 'Multiple of?' the computer would print '5X' since 24 is not a multiple of 5. If you chose 8 it would print '8' on the screen since 24 is a multiple of 8. This is the only clue that may be chosen more than once. It may be used up to four times. Each time a clue is chosen you are given the opportunity to make a guess. After the guess has been entered the computer will tell you if you are correct. If you are incorrect each guess that you make will be displayed at the bottom of the screen. Each time a clue is selected the number of points is reduced by the cost of the clue. If you run out of points your turn will end. 10 LEARN TO GUESS (c) 1988 D. Bodnar SUPERGUESS - Part 2 Once you have successfully found the secret number you will be shown the second game screen. This screen shows a square board with randomly chosen barriers through it. Your task is to move across the board from the side where your name is displayed to the opposite side before any of your opponents move across the board. On the left side of the screen you will see the words Blast and Escape. Next to the words a vertical line indicates how far the points that you have remaining will take you across the board. Use the arrow keys to move the flashing cursor from the side of the board with your name to the opposite side. Holding an arrow key will cause it to repeat. When you come to a barrier, one placed there by the computer or an opponent's line, you may go around it or, if you have at least 20 points remaining, through it. To go through a barrier line you must move up to it, as close as you can get, and press the B key. B stands for Blast and it allows you to expend 20 points at one time to blast through a line. Once B has been pressed a buzzing sound will be heard. At this point you must press one arrow key and you will be moved one space in that direction regardless of what is in your path. Once you use blast the vertical line that shows your remaining points shrinks significantly since each blast uses 20 points. Once your points are exhausted your turn is over and the game continues until someone makes it to the other side. If you should come up against a barrier and not have sufficient points to blast you may press the E key to escape and save your points for the next turn. At the end of each round you will see the current standings displayed. They show how far each player has moved and, after the '+' sign, any points that they have saved by using escape. Three start indicate the player or players who lead. The game is over when one or more players reach the far side of the board. A winner is not declared until each player has completed a round of play. 11