Exercise 2: Finding an Input Where the Two Thick Clients Agree — Possible Solution
====================================================================

A SEARCH ACROSS SEVERAL INPUTS
------------------------------
Running both this chapter's own mobile_client_calculate_total() and
web_client_calculate_total() across a range of items_total values (all
for a loyalty member) found:

    items_total=50:  mobile=45.0, web=45.0,  agree=True
    items_total=80:  mobile=72.0, web=72.0,  agree=True
    items_total=90:  mobile=81.0, web=81.0,  agree=True
    items_total=95:  mobile=85.5, web=85.5,  agree=True
    items_total=100: mobile=90.0, web=90.0,  agree=True
    items_total=101: mobile=90.9, web=86.4,  agree=False
    items_total=120: mobile=103.0, web=103.5, agree=False

items_total=90 is a clean example: both clients return 81.0.

WHY THE BUG DOESN'T SHOW UP FOR THIS INPUT
------------------------------
Both functions share one conditional branch: "if total > 100, subtract
$5." At items_total=90, the loyalty discount alone (90 * 0.90 = 81)
never pushes the running total above 100 - so the $5-off branch is
simply never entered by EITHER client, regardless of which order the
two rules are checked in. With only one of the two rules ever actually
firing, there's no ordering for the two clients to disagree about -
the mobile and web implementations only diverge when BOTH rules are
live at once, which requires the discounted total to cross the $100
threshold specifically because of which rule ran first.

THE GENERAL PATTERN THIS REVEALS
------------------------------
This chapter's own $120 example (mobile=103.0, web=103.5) worked
specifically because 120 is high enough that the order the two rules
run in changes whether the $5-off condition (total > 100) is still
true by the time it's checked. Every value at or below 100 sidesteps
the bug entirely; every value comfortably above 100 (verified at 101,
105, 110, 111, 120, 150, 200) triggers it. This means the two thick
clients agree on MOST small orders and disagree on most larger ones -
a bug that's easy to miss in casual testing with small example orders,
and easy to hit in production once a real customer places a large one.

WHY THIS WORKS AS AN ANSWER
------------------------------
A genuinely agreeing input is found and verified directly rather than
assumed to exist, and the explanation for why it agrees is traced to
the specific conditional structure shared by both functions, rather
than treating it as a coincidence.