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#### Johnny’s dad had told Johnny that if he could get an A+ on his final exam, he could get any ice cream flavor he wanted plus a pizza. When the day for the final exam came, the professor said, “There are three questions on this exam. You will have one hour to answer them all and no more. Anyone caught taking any longer or cheating will get an automatic F.” When Johnny received the paper, he read the first question. As he read it, he realized the exam was no piece of cake so he worked as hard as he could. When he finally finished question one, he checked the clock. There was only 5 minutes left! At this rate, he wouldn’t be able to finish in time. As Johnny looked around, he saw that there were hundreds of students and figured that he could get away with a few extra minutes, so he worked away past the hour mark. As Johnny went to turn in his paper, the professor stopped him. “Young man,” the professor said sternly. “I saw you keep working long after the 1-hour mark. You were caught cheating and will get an F.” Thinking quickly, Johnny replied, “Do you know who I am?” The professor stoically responded, “I neither know or care who you are. You need to learn respect and discipline.” “Good.” said Johnny and he ran away. When the day for the exam scores to be announced came, Johnny received an A+. How?

**Answer: ** When the professor confirmed Johnny's anonymity (the professor didn't know who he was), Johnny quickly slipped his exam paper into the pile of exams and ran off, so the professor wouldn't know which exam paper deserved an F. Congratulations on sticking through the whole riddle.

**Solution: **

#### The title of the problem tells you how to approach these four questions. (A). A bus leaves Moscow for Tula at noon. An hour later a cyclist leaves Tula for mosco, moving slower than the bus. When the bus and cyclist meet, which one of the two will be farther from Moscow? (B). Which is worth more: a pound of $10 gold peices or half a pound of $20 gold pieces? (C). At six o’clock the wall clock struck 6 times. Checking with my watch, I noticed the time between the first and last strokes was 30 seconds. How long will the clock take to strike 12 at midnight? (D). Three swallows fly outward from a point. When will they all be on the same plane in space? Now check the answers. Did you fall into any of the traps which lurk in these simple problems?

**Answer: ** (A). Neither
(B). A pound of metal is always more than half a pound of the same metal.
(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.
(D). There is always a plane that contains any 3 points

**Solution: **

## Show Answer

(A). Neither

(B). A pound of metal is always more than half a pound of the same metal.

(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.

(D). There is always a plane that contains any 3 points

## Show Answer

(A). Neither

(B). A pound of metal is always more than half a pound of the same metal.

(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.

(D). There is always a plane that contains any 3 points

(B). A pound of metal is always more than half a pound of the same metal.

(C). Six strokes took 30 seconds, therefore 12 strokes will take 60 seconds. But when the clock struck six, there were only 5 intervals between strokes, and each interval was 30/5=6 seconds. Between the first and twelfth strokes there will be 11 intervals of 6 seconds each, therefore 12 strokes will take 66 seconds.

(D). There is always a plane that contains any 3 points

#### Emily was gossiping with her friends and told them that she was sure Josh was a drunk because she always saw his car parked in front of the bar. Josh overheard this and decided he was going to use his car to get back at her by making everyone think she was easy. How did he do this?

**Answer: **He parked his car in front of Emily’s house and left it there all night, night after night

**Solution: **

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