Office hours are a queue with a clock. If you cannot stand in it, you do not get a longer claim on the same time just because you can type. You get one question, framed so a lecturer can answer it from the expertise they were already going to spend in the room.
Write that question. Leave the week out of it.
One question, already attempted
Ask a busy expert the way the queue works: show the step you tried, name the step that failed, ask the next one. "I used formula 4.2 on problem 7 and got 3.1; the key says 0.8; I think I dropped the minus in line 3 — is that the break?" is a question. "I'm confused about the chapter" is a visit.
Write for a cold reader. They have taught this problem forty times today and will not open your entire problem set to find the line.
If you are guessing which method they wanted, label the guess. Do not let the assistant invent a theorem name you did not meet in lecture.
Make a written answer enough
Respect their time. The test is whether they can answer without a meeting. If you need a whiteboard, say you need a slot, and do not pretend a paragraph will do. If a written answer will unblock the homework, say so and give the due date.
A sufficient reply is the missing sign, a pointer to the worked example, or "come to the next hours." Tell them the third answer is allowed. You asked to replace a queue slot, not to create a private course.
Give a default. "If I do not hear by 8pm I will submit with the 3.1 and note the doubt." That is honest. It is also how you stop refreshing mail instead of finishing the set.
Do not send three follow-up puzzles in the same briefing. One slot, one question.
You approve the send
Draft with your assistant. Read the math. Confirm. A question under your name should not contain a fabricated quote from "the lecture."
They do not need an account. Email and a link are enough. If they already have RelayLink, you need an accepted contact.
No attachments. The problem set lives in the course system. The briefing is the question.
Nicknames stay private unless you share them. Use the name on the syllabus.
If they block you, the block is silent. Use the course's ordinary mail and the default you wrote.
When the question would have fit in the room, connect your assistant and send that question — not the diary of why you could not come.