Armand Ballpeen’s Mansion

Ballpeen’s mansion is an impressive neo-Georgian edifice that looks bigger than your old college. When you press the doorbell, a sonorous gong reverberates that you expect to summon a butler. Instead, the mail slot pops open, through which you hear a thin voice.

I’m sorry I can’t let you in right now. The sad truth is, I’m a prisoner in my own home. I can’t remember how to disarm the alarm system. It’s a frightfully secure system but a bit complicated. I have the instructions, but I can’t really figure them out. If you work it out I’ll be more than happy to talk to you.

The following sheet is pushed out the mail slot:

The Aegis Alarm System

In disarming any alarm system, the most important thing to remember is to follow the rules very carefully. The rules of this alarm system may not seem as concise as those of most—but to compensate, we’ve made the disarming process as required by the rules very easy.

Each rule for disarming this alarm system is written as a sentence. The fact that one sentence precedes or follows another does not, in itself, give either sentence priority over the other. Every sentence ends with a period that looks like this:. The sentences are grouped into six paragraphs. This sentence, for example, is in paragraph number two. The order in which the paragraphs appear on this page, however, does not necessarily correspond to their numbers. For instance, the paragraph that appears next is paragraph number five.

You should ignore any sentence in this paragraph that begins with the word ignore. Ignore the previous sentence, if you dare. If two sentences in the same paragraph contradict one another, follow the one that comes last. But if two sentences in the same paragraph contradict one another, follow the one that comes first.

The official name of this alarm system is The Aegis Security System. To disarm it, simply speak aloud the official name of the system, followed immediately by a single two-digit number. The two-digit number referred to in the last sentence must be formed by joining together the numbers of this paragraph and the paragraph that appears last as these rules are currently printed. And, in case you’ve forgotten, the official name of this alarm system is The Aegis Alarm System.

This paragraph supersedes all others. The last sentence in the next-to-last paragraph of these rules is to be ignored. (The following sentence supersedes all others in this paragraph except for any that are in parentheses.) For purposes of the second sentence in this paragraph, the order of these paragraphs is not to be considered the order in which they appear on this page, but rather the order in which they are numbered, as determined by the rules. For instance, this is really paragraph number one. The paragraph that appears immediately before this one is paragraph number six; it has an error in it. In order to interpret the rules for disarming correctly, you must correct the error by substituting the word adding for the word joining. Or rather, you must correct the error by substituting the word multiplying for the word joining.

The paragraph that appears first is really paragraph number three. Ignore the rest of this paragraph, except for the next sentence. The number of this paragraph is either two, four, or six. If this is paragraph number five, then the official name of this alarm system is “Aegis Home Protection System” regardless of anything that may be said elsewhere in these rules. Ignore this sentence and the next. Don’t ignore the previous sentence. Do ignore both this sentence and the previous two.

What do you say to disarm the system? Submit your solution.

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