Defensive. The purpose is to quickly establish implausibility of a result.
Example: compute 91·18. Answer: 91·18 = 1538. This is obviously wrong because 18 is divisible by 9 and so must be the product 91·18.
On the other hand, 1538 is not divisible by 9 since its digits sum up to 1 + 5 + 3 + 8 = 17 which is not divisible
by 9. The correct answer is 1638.
Entertaining. The purpose is to stun with the ability to produce a result as much as with the result itself.
Example: Think of a 3-digit number. Write it in reverse. Subtract the smaller of the two from the larger one. Give me the first two digits of the result. I'll respond with the remaining digit.
