[image] GUESS [image] GUESS is a simple introduction to the idea of a computer program and computer games. It also introduces the notions of comparison and searching a list. Before playing GUESS on the computer, you may wish to play it in class at the chalkboard. One student is selected to be the computer. He is given the flowchart below and is asked to follow it and write on the chalkboard the statements in parentheses as well as each guess. Students take turns being the computer. [image] FLOWCHART START CHOOSE ANY NUMBER BETWEEN 1 AND 100 WRITE ON CHALKBOARD, "I'M THINKING OF A NUMBER" WRITE ON CHALKBOARD, "WHAT'S YOUR GUESS?" ACCEPT GUESS FROM CLASS MEMBER AND WRITE IT ON THE CHALKBOARD COMPARE GUESS TO NUMBER WRITE "TOO HIGH" WRITE "YOU GOT IT!" WRITE "TOO LOW" STOP [image] After playing the game manually, play GUESS on the computer. Divide the class into small teams of 2 or 3 members each. Have each team play 10 games on the computer and keep track of the number of guesses required to get each number. Compute the average guesses for each team and for the entire class. After playing the class should consider the following questions: 1. Why should it never take more than 7 guesses to find the number? 2. What was the average guesses for the class? How does this compare to the theoretical average (using the correct guessing strategy) of 5.3? 3. What are the maximum number of guesses required to find a mystery number between: 1 and 10 1 and 64 1 and 63 1 and 1000 PROGRAM LISTING 1 PRI "THIS IS A NUMBER GUESSING GAME. I'LL THINK" 2 PRI "OF A NUMBER BETWEEN 1 AND ANY LIMIT YOU WANT. " 3 PRI "THEN YOU HAVE TO GUESS WHAT IT IS." 4 PRI 5 PRI "WHAT LIMIT DO YOU WANT" 6 INPL 7 PRI 8 L1=INT(LOG(L)/LOG(2))+1 10 PRI "I'M THINKING OF A NUMBER BETWEEN 1 AND"L 11 G=1 14 PRI "NOW YOU TRY TO GUESS WHAT IT IS" 15 M=INT(L*RND(0))+1 20 INP N 21 IF N>0 THEN 25 22 GOSUB70 23 GOTO1 25 IF N=M THEN 50 30 G=G+1 31 IF N>M THEN 40 32 PRI "TOO LOW. GUESS AGAIN. " 33 GOTO 20 40 PRI "TOO HIGH. GUESS AGAIN. " 42 GOTO20 50 PRI "THAT'S IT! YOU GOT IT IN*G*TRIES. 52 IF G<L1 THEN 50 54 IF G=L1 THEN 60 56 PRI "YOU SHOULD HAVE BEEN ABLE TO GET IT IN ONLY*L1* 57 GOT 65 58 PRI "VERY "; 60 PRI "GOOD! 65 GOSUB70 66 GOTO10 70 FOR H=1 TO 5 71 PRI 72 NEXT H 73 RETURN 99 END Note: BASIC statements in this program are abbreviated to their first 3 letters. SAMPLE RUN THIS IS A NUMBER GUESSING GAME. I'LL THINK OF A NUMBER BETWEEN 1 AND ANY LIMIT YOU WANT. THEN YOU HAVE TO GUESS WHAT IT IS. WHAT LIMIT DO YOU WANT? 100 I'M THINKING OF A NUMBER BETWEEN 1 AND 100 NOW TRY TO GUESS WHAT IT IS. ? 50 TOO HIGH. GUESS AGAIN. ? 25 THAT'S IT! YOU GOT IT IN 2 TRIES. VERY GOOD! I'M THINKING OF A NUMBER BETWEEN 1 AND 100 NOW TRY TO GUESS WHAT IT IS. ? 50 TOO HIGH. GUESS AGAIN. ? 25 TOO LOW. GUESS AGAIN. ? 37 TOO HIGH. GUESS AGAIN. ? 31 TOO HIGH. GUESS AGAIN. ? 28 TOO LOW. GUESS AGAIN. ? 29 TOO LOW. GUESS AGAIN. ? 30 THAT'S IT! YOU GOT IT IN 7 TRIES. GOOD!