Thomas the Truant (Winter 2014)

Puzzle:

Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him, “Why on Earth have you missed so many days?”

Thomas replies: “There just isn’t enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days.If I spend about an hour on each meal, that’s 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days. Add all of that up and you get about 361 days. That only leaves 4 days for school.”

The principal knows Thomas is full of it, but can’t figure out why. Why is Thomas wrong?

Solution:

First, Thomas is double counting a lot of the days. A lot of the time spent sleeping, eating, and relaxing occurs during weekends and the summer. Weekends also occur during the summer, so all of these hours are getting counted several times. Secondly, school isn't an all day thing. So the 4 days actually represents more days of school. If school is 6 hours per day, those four days represents 16 days of school.

(SOURCE: Good Riddles Now)

OUR COLUMBUS PROBLEM (FALL 2014)

Puzzle:

In 1882, American chess player and puzzle writer Samuel Loyd issued a challenge to the public worth $1,000 (which is $22,727.27 USD today ). Out of several million answers, only two were found to be correct. Give it a try, show how to arrange the seven figures and the eight “dots”—.4.5.6.7.8.9.0.—to add up to 82.

Solution:

A dot over a number signifies that it is a repeater which would go on for ever, as when we endeavor to describe 1/3 decimally as 0.33333 . . . . (etc). With a series of numbers we place the dot over the first and last, as with 0.97979797979 . . . (etc). The remarkable feature here is that a proper fraction divided by 9s (eg. 46/99) is exactly equal to the numerator with the repeater sign followed by the decimal. So, as per the mathematical truths above, one solution is : 80 + .55.... + .9797.... + .4646.... = 80 + 55/99 + 97/99 + 46/99 = 80 + 198/99 = 82).

(SOURCE: Math Is Fun)

 

THE CONTESTANT (SUMMER 2014)

Puzzle:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a sports car; behind all of the others are bicycles. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens door No. 2, revealing a bicycle. He then says to you, "Do you want to pick door No. 3?" Is it to your advantage to switch your choice?

Solution:

Yes, by changing your answer your chances of winning actually goes up from 1/3 to 2/3. This becomes obvious when expanding the example. Suppose there was 100 doors rather than 3. You pick one and the host shows you that the car is not behind 98 of the doors then asks you to switch to the remaining door or keep the door you picked. Of course you would switch your door because chances are you didn't pick the correct door initially. (This is a Monty Hall problem).

(SOURCE: Good Riddles Now)

FOOT RACE (SPRING 2014)

Puzzle:

Two boys, Trevor and Tyler, are running a 100-meter race. The first time they race Trevor beats Tyler by five meters. To make things fair, the next time they race Trevor stands five meters behind the starting line. Who wins the second race (assuming they run the same speed as the first race)?

Solution:

Trevor wins again. In the first race, Trevor ran 100 meters in the time it took Tyler to run 95 meters. So, in the second race when Tyler is at the 95 meter mark, Trevor will also be there (since 100 - 5 = 95). Since Trevor is faster, he will pass Tyler in the last 5 meters of the race.

(SOURCE: Good Riddles Now)