PLEASE ONLY DO QUESTION $2$ IN PYTHON in grading homework $5$ I noticed a variety of solutions to question $10($print all numbers between $1000$

and $3000,$ inclusive, where each digit is even$).$ I appreciate questions like this for it allows me to see a

range of thinking on how to solve a problem. Here are two solutions that were given:

print$(*[$n for n in range$(1000,3001)$ if all$([($int$($c$)\%2==0)$ for c in str$($n$)])],$ sep$=\text{'},\text{'})$

for i in range$(1000,3001)$:

is$\_$even $=$ true

for j in str$($i$)$:

if int$($j$)\%2==1$:

is$\_$even $=$ false

if is$\_$even:

numbers.append$($i$)$

print$($numbers$)$

The second solution takes more coding but essentially does the same thing. Part of writing software

$($or doing analysis, at least$)$ is identifying patterns of what needs to be done. Making a problem

generic can sometimes help in this regard $($find numbers between x and y$,$ etc.$).$ Looking at a

problem in a different way $($thinking outside of the box$)$ can provide a unique solution as well. One

thing to always remember is that just because something is a number doesn't mean it has to be

treated as a number. Think of phone numbers or social security numbers. While they contain only

digits, one almost never performs mathematical operations against them so they could just as easily

be strings, and probably should be$.$

The two solutions above are more efficient than examining every number between $1000($or x$)$ and

$3000($or y$),$ but they could be more efficient yet. Think about what problem we're trying to solve. The

first solution is probably a good one, but is there a better one? If the $10\text{'}$s position contains an odd

number, does it matter what the digit is in the one's position? No$,$ so we should move to the next $10\text{'}$s

position value. The same holds true for $100\text{'}$s and $1000\text{'}$s positions.

Q$1[10$ pts$].$ Determine how to time programs in Python. Run $3$ tests of each of the first two solutions

given above and average the results. Come up with a solution that is more efficient $($faster$).$ Run $3$

CIS $298$

$2$

tests on it and record the average. Supply your faster algorithm and the average result of all three

algorithms.

Q$2[50].$ Deep dive into logically cutting corners in a solution through analysis. Find a solution to this

problem that executes in under $1$ second $($can it be even faster?$)$ without hardcoding the

answer. Displaying values takes a long time so remove most output statements once you$$re getting

close. I'll spare you the long version of the question. Simply do this: find the price of four items who's

sum and who's product both equal $7\mathrm{.}11.$ So$,$ a$+$b$+$c$+$d $==$ a$*$b$*$c$*$d $==7\mathrm{.}11.$ There may be more than

one answer. I originally solved this problem $42$ years ago $($in C$).$ My initial algorithm ran for over $12$

hours. My deep dive analysis produced one that solved it in about $1$ second. Supply your final

algorithm and how long it takes to solve the problem $($using the average of three runs$).$