# [plt-scheme] Combining digits to form numbers

On Feb 16, 2009, at 2:59 PM, aditya shukla wrote:
>* I am trying to solve this exercise from htdp ...
*
Yes, I like that exercise, and I've given it to my students on a
number of occasions. Which is one reason for not giving you a
solution to it on an e-mail list :-)
However, I can suggest a general technique that helps here as well as
in many other problems. Assuming you've already seen "templates" or
"inventories", a step of program design in which you write down what
you have available (mostly parameters to the current function) and
their types, I call this technique "Inventories with Values".
Suppose you've already got
; convert-3-digits : number (lsb) number (csb) number (msb) -> number
(check-expect (convert-3-digits 0 0 0) 0)
(check-expect (convert-3-digits 1 2 3) 321)
(check-expect (convert-3-digits 5 1 0) 15)
(check-expect (convert-3-digits 2 9 7) 792)
(define (convert-3-digits lsb csb msb)
; lsb a number, 0-9
; csb a number, 0-9
; msb a number, 0-9
...
)
Pick a moderately-complicated one of your examples; let's try the
last one, 792. For each item in your inventory, write down not only
its type but its VALUE FOR THIS EXAMPLE. Also add a line to the
inventory labelled "Right Answer", with ITS value for this example.
; convert-3-digits : number (lsb) number (csb) number (msb) -> number
(check-expect (convert-3-digits 0 0 0) 0)
(check-expect (convert-3-digits 1 2 3) 321)
(check-expect (convert-3-digits 5 1 0) 15)
(check-expect (convert-3-digits 2 9 7) 792)
(define (convert-3-digits lsb csb msb)
; lsb a number, 0-9 2
; csb a number, 0-9 9
; msb a number, 0-9 7
; right answer a number 792
...
)
Now the challenge is to use your human pattern-recognition abilities
to figure out how to get to the "right answer" from the available
expressions. Since everything in sight is a number, the most likely
operations are arithmetic: +, -, *, /. What arithmetic expression
involving 2, 9, and 7 would give you 792? (You might want to try an
example with msb=0 first.)
Stephen Bloch
sbloch at adelphi.edu