Editing Openai/691cc483-9e74-8006-a4a7-7e5bbf8a5391 (section)

=== Assistant: Alright, let’s cut straight through it. ===
Alright, let’s cut straight through it.

What’s happening?
They keep picking two numbers and replacing them with (sum − 2). That means:
* Every operation reduces the total sum by exactly 2.
* They start with numbers from 3 to 89, inclusive.

===== Step 1 — Count how many numbers there are =====

From 3 to 89:

89−3+1=87 numbers89 - 3 + 1 = 87 \text{ numbers}89−3+1=87 numbers
To end with one number, they must do:

87−1=86 operations87 - 1 = 86 \text{ operations}87−1=86 operations
===== Step 2 — Compute the initial sum =====

Sum of an arithmetic progression:

S=(3+89)⋅872S = \frac{(3+89)\cdot 87}{2}S=2(3+89)⋅87
=92⋅872=46⋅87=4002= \frac{92 \cdot 87}{2}
= 46 \cdot 87
= 4002=292⋅87=46⋅87=4002
===== Step 3 — Decrease the total sum =====

Each operation subtracts 2, and there are 86 operations:

4002−2⋅86=4002−172=38304002 - 2\cdot 86 = 4002 - 172 = 38304002−2⋅86=4002−172=3830
===== Final answer: =====

3830

That’s the last number standing.