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How about a "guess the number 099" program for the 17b (and 17bii) solver.
At first glance, you would think it might not be possible due to: lack of a random number function, lack of alpha messages to tell you if you are too high or too low, and lack of a "beep" instruction when you correctly guess the number. Plus, the 17b is not programmable, right?
Lack of random number function is overcome by using current time (minutes, seconds) and the MOD function. Lack of alpha capability is overcome by returning 1 if your guess is too low and 1 if it is too high (yes, it's not ideal, but it works). A "beep" is generated by doing a Log(0) which generates an error message and halts evalution of the equation (AFTER saving the number of guesses in variable GUESS so it can be recalled).
The equation works on the 17b and 17bii. It mostly works on the 17bii+ except the number of guesses is wrong due to the way the solver in the 17bii+ works (or doesn't work, actually).
IF(S(INIT):
L(G:0)X
L(N:MOD(10000XFP(CTIME)X111:100))
INIT
:
0XL(G:G(G)+1)+
IF(GUESS=G(N):
L(GUESS:G(G))+
LOG(0)
:
IF(GUESS>G(N):1:1)
)
EVAL
)
Press INIT a couple of times (not sure why that is necessary) then enter your guess and press GUESS. Then press EVAL to evaluate your guess: 1 means you are too low, 1 means you are too high, and a beep means you guessed the number so do a RCL GUESS to see the number of guesses it took.
What is the maximum number of guesses it should take to identify the number from 0 to 99?
Edited: 7 June 2011, 8:31 p.m. after one or more responses were posted
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Quote:
What is the maximum number of guesses it should take to identify the number from 0 to 99?
7? (100 LN 2 LN /)
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Implementing the TI 58/59 game described below on an RPN HP calculator is trivial. Now doing it on the HP17B is not. Congratulations!
From the TI Programmable 58/59 Master Library Manual, page 77:
HILO GAME ML21
In addition to recreational diversion, this program serves as a nontechnical demonstration of the library
module. The game is easy to play, permitting almost immediate handson experience for any user.
The object of the game is to guess a secret number (whole numbers only) from 1 to 1023 that has been
generated in the calculator. The calculator responds with a "too high," "too low," or "correct" indica
tion to each of your guesses. Your score (number of guesses) is tallied by the calculator.
Also, you may select a number in the range 1 to 1023 and the calculator will attempt to guess this
number as you supply proper responses to each of its guesses. When the calculator has found the num
ber you selected, its score will be displayed.
An exercise which often cast doubt on the "man over machine" axiom is to have the calculator guess
the same number that it generated for you to guess. Now, follow the User Instructions and seed if you
can uphold the superiority of man.
USER INSTRUCTIONS
STEP PROCEDURE ENTER PRESS DISPLAY
1 Select program 2nd Pgm 21
You Guess
2 Key in number (0 to 199017)* Number A Number
3 Generate secret number B 0.
4 Enter your guess (1 to 1023) Guess C Clue
Clue: 1. if guess was low
1. if gues was high
flashing 0. if your guess was correct
5 Repeat Step 4 as required
6 Display score D Score
7 For a new number, go to Step 3
Calculator Guesses
8 Select a number (1 to 1023)
9 Display calculator's first guess 2nd A' Calc. guess
10 If calculator's guess is
Low 2nd B' Calc. guess
High 2nd C' Calc. guess
Correct 2nd D' Calc. guess
11 Repeat Step 10 as required
12 For a new game, go to Setp 8
*Each number you select will produce a different game.
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The 17b solver is not the best platform for this particular game, I just wanted to see if it could be done in a way that wasn't too horrible. It is more intuitive on a regular RPN calculator; for example, you enter your guess and press R/S and it immediately tells you "too high" or "too low" (on models like the 30b that have alpha messages). The 17b requires another keypress to get that feedback.
I like to discuss this problem with my students. They are always kind of amazed that a maximum of only 7 guesses can identify a selected number from 0 to 99 when I show them the advantages of splitting the groups in half each time, thus narrowing down the potential set of numbers. It kind of makes math interesting, if only for a moment!
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Quote:
They are always kind of amazed that a maximum of only 7 guesses can identify a selected number from 0 to 99 when I show them the advantages of splitting the groups in half each time, thus narrowing down the potential set of numbers.
In the example at the next page in the TI manual the program is asked to find a secret number, 848. The program's guesses, following the user's correct clues, are 512, 768, 896, 832, 864 and 848, that is, 512, 512+256, 512+256+128, 512+256+12864, 512+256+12864+32 and 512+256+1286416. That's the principle behind the binary search algorithm. Once I used this technique to find a fault in an 800meter long circuit in four or five steps. The idea occurred to me from having played this little game. Thanks for bringing it back :)
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The 20b SDK by Cyrille and Tim is designed just around this game. :)
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I have used the hilow guessing games in many programmings books that I wrote way back. I would present various versions, each a bit more sophisticated than the previous one.
One interesting (and cunning) variation of the hilow game is the percent of reliability for the feedback. Normally, the program would reliably tell you if your guess is higher or lower than the secret number. This special variant would introduce a level of doubt (say 10%) in that kind of answer, making thinks a bit more interesting.
Namir
Edited: 7 June 2011, 7:49 p.m.
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I think "Jive Turkey" was the name the TI user group put on that variety of HiLo game.
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Quote:
I would present various versions, each a bit more sophisticated than the previous one.
Namir,
Would you mind posting a couple of listings here? Thanks!
Gerson.
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Here is a QBasic listing (also runs on 64bit QB64):
REM HiLO GUESSING GAME
DIM Num AS INTEGER, Guess AS INTEGER
DIM Iter AS INTEGER, MaxIter AS INTEGER
DIM Trust AS DOUBLE
RANDOMIZE TIMER
MaxIter = 10
Num = INT(1000 * RND(1) + 1)
Iter = 0
INPUT "Enter feedback trust (%) "; Trust
Trust = Trust / 100.0
DO
INPUT "Enter Guess"; Guess
Iter = Iter + 1
IF Trust > RND(1) THEN
REM TRUE FEEDBACK
IF Guess > Num THEN
PRINT "Your guess is high"
ELSEIF Guess < Num THEN
PRINT "Your guess is low"
ELSE
PRINT "You guess it!"
END IF
ELSE
REM MISLEADING FEEDBACK!!
REM (unless you guess the secret number)
IF Guess < Num THEN
PRINT "Your guess is high"
ELSEIF Guess > Num THEN
PRINT "Your guess is low"
ELSE
PRINT "You guess it!"
END IF
END IF
LOOP UNTIL Num = Guess OR Iter > MaxIter
IF Iter <= MaxIter THEN
PRINT "Solved it in "; Iter; " guesses"
ELSE
PRINT "Time out! Secret number is "; Num
END IF
Edited: 8 June 2011, 12:22 a.m. after one or more responses were posted
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Well, a little testing with VBScript has determined that the method I used to generate a random number between 0 and 99 is totally unacceptable. Whole series of numbers, such as 14, 1215, 2326, etc., are never generated by that method. So I came up with a new method using the first 2 digits of the fractional part of the square root of mmss returned by the CTIME function, and that method does generate every number from 0 to 99 in a more or less random method, good enough for an entertainment program.
This is the new program:
IF(S(INIT):
L(G:0)X
L(N:IP(100XFP(SQRT(10000XFP(CTIME)))))
INIT
:
0XL(G:G(G)+1)+
IF(GUESS=G(N):
L(GUESS:G(G))+
LOG(0)
:
IF(GUESS>G(N):1:1)
)
EVAL
)
