Saying why, in order
The reverse trick works — but can you say why, in order?
- Four sentences, jumbled: Answer, Reverse, Number, Subtract.
- Number needs nothing. Place it first.
- Reverse needs the number. Place it next.
- Subtract needs both. Answer needs subtract. In order: Number, Reverse, Subtract, Answer.
An argument, in the maths sense
Yes. Let a be the tens digit and b the ones digit. The number is 10a + b. Its reverse is 10b + a. Four short sentences give the reason, each using only earlier ones.
Two people arguing are disagreeing. Here the word means something else. An argument is a list of sentences. Each sentence gives the listener one more step.
The rule
Each sentence may use only what earlier sentences said. A sentence that needs a fact not yet said must move later.
In the list below, "ten of" a digit means 10 times it. "Nine of" a digit means 9 times it.
The reason for reverse and subtract, in an order that works:
- The number is ten of its tens digit, plus its ones digit.
- The reverse has ten of the ones digit, plus the tens digit.
- Subtracting leaves nine of one digit, less nine of the other.
- That is nine times the gap between the two digits.
Steps 1 and 2 must come before step 3. Step 3 subtracts the smaller number from the bigger.
Check step 3 on 52. Nine of 5 is 45. Nine of 2 is 18. 45 − 18 = 27.
An example like 52 − 25 = 27 is not a step. It checks one case. It does not prove every case.
Tap the sentence that comes next. A sentence that needs a missing fact is refused.
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