You have the misfortune to own an unreliable clock. This one loses exactly 8 minutes every hour. It is now showing 4:15pm and you know that is was correct at midnight, when you set it. The clock stopped one hour ago, what is the correct time now?
Answer: 7:45pm: since the clock is losing 8 minutes every hour, for every real hour that has passed, the clock will only show 52 minutes. Since the clock shows 4.15pm, we know that 975 clock minutes have passed. This therefore equals 1125 real minutes and hence 18 hours 45 minutes. The clock stopped 60 minutes ago, therefore the time must now be 19.45pm. QED.
On my local railway track there is a tunnel which is 5 miles long.
A train, which was 440 yards long, entered the tunnel at a speed of 50 miles per hour.
How long did it take for the whole of the train to pass completely through the tunnel?
Hint: There are 1,760 yards in a mile.
Answer: 6 minutes and 18 seconds.
The train has to effectively travel 5.25 miles at 50 mph. Time = Dist ÷ Speed = 5.25 ÷ 50 = 0.105 hours = 6.3 minutes = 6 minutes 18 seconds. QED.
Last week I decided to cycle to my Grandmother's house.
On the first day, I cycled half of the distance.
On day 2, I cycled one half of the remaining distance.
On day 3, I cycled three quarters of the remaining distance.
On day 4, I cycled 10 miles.
On day 5 I cycled two thirds of the remaining distance and on the final day I cycled the remaining 5 miles.
On the final day I cycled the remaining 5 miles
On Day 5 I started with 15 miles (as I cycled two thirds, leaving 5 miles).
On Day 4 I started with 25 miles (as I cycled 10 miles).
On Day 3 I started with 100 miles (as I cycled three quarters, leaving 25 miles).
On Day 2 I started with 200 miles (as I cycled half, leaving 100 miles).
On Day 1 I started with 400 miles (as I cycled half, leaving 200 miles).
Two boxes are labelled "A" and "B".
A sign on box A says "The sign on box B is true and the gold is in box A".
A sign on box B says "The sign on box A is false and the gold is in box A".
Assuming there is gold in one of the boxes, which box contains the gold?
Hint: This is a mind-bending paradox.
Answer: The problem cannot be solved with the information given.
The following argument can be made: If the statement on box A is true, then the statement on box B is true, since that is what the statement on box A says. But the statement on box B states that the statement on box A is false, which contradicts the original assumption. Therefore, the statement on box A must be false. This implies that either the statement on box B is false or that the gold is in box B. If the statement on box B is false, then either the statement on box A is true (which it cannot be) or the gold is in box B. Either way, the gold is in box B.
However, there is a hidden assumption in this argument: namely, that each statement must be either true or false. This assumption leads to paradoxes, for example, consider the statement: "This statement is false." If it is true, it is false; if it is false, it is true. The only way out of the paradox is to deny that the statement is either true or false and label it meaningless instead. Both of the statements on the boxes are therefore meaningless and nothing can be concluded from them. Common sense dictates that this problem cannot be solved with the information given. After all, how can we deduce which box contains the gold simply by reading statements written on the outside of the box? Suppose we deduce that the gold is in box B by whatever line of reasoning we choose. What is to stop us from simply putting the gold in box A, regardless of what we deduced?