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The easiest way to solve this puzzle is to use Q1 to check the logic.
If Q1's answer was A, this tells us that Q2's answer is B, which tells us Q3's is D, which tells us Q4's answer is B, which tells us Q1's answer is C. A contradiction.
If Q1's answer was B, this tells us that Q2's answer is A, which tells us Q3's is C, which tells us Q4's answer is C, which tells us Q1's answer is A. A contradiction.
If Q1's answer was C, this tells us that Q2's answer is D, which tells us Q3's is A, which tells us Q4's answer is D, which tells us Q1's answer is B. A contradiction.
If Q1's answer was D, this tells us that Q2's answer is C, which tells us Q3's is B, which tells us Q4's answer is A, which tells us Q1's answer is D. Which is correct, and therefore the correct answer.
Raise each to the power of 30 (since 10 x 3 = 30) to give:
10^{1/10 x 30} vs 2^{1/3 x 30}, which simplifies to:
10^{3} vs 2^{10}, which gives:
1000 vs 1024.
Therefore the cube root of 2 is larger. Alternatively we can use a calculator to see that the tenth root of 10 = 1.2589 and the cube root of 2 = 1.2599.
Puzzle 3
I recently went to the shop and purchased 4 items.
Three of the items cost:
$1.50
$3.00
$4.00
There was quite a long queue, and as I was quite bored, I was playing with my pocket calculator whilst waiting.
Very curiously, the 4 prices added to the same number as I got when I multiplied the 4 prices together.
Hint: What do the 3 numbers add and multiply to give so far?
Answer: $0.50.
The three prices add to 1.50 + 3.00 + 4.00 = 8.50.
The three prices multiply to 1.50 x 3.00 x 4.00 = 18.00.
You might be able to see that adding another 0.50 will take the total to 9.00, and multiplying by another 0.50 will take the product to 9.00.
The answer can also be found using algebra. If we call the missing price P, we have:
1.50 + 3.00 + 4.00 + P = 1.50 x 3.00 x 4.00 x P
8.50 + P = 18.00 x P
8.50 = 18.00 x P  P
8.50 = 17.00 x P
8.50 ÷ 17.00 = P
P = 0.50.
Puzzle 4
You want to send a valuable object to a friend.
You have a box which is more than large enough to contain the object.
You each have several locks with keys, but not keys to each other's locks.
The box has a locking ring which is large enough to have many locks attached.
You cannot send a key in an unlocked box, since it might be copied.
How do you do it?
[Ref: ZWOK]
Hint: Just two locks are required.
Answer:
Attach a lock to the ring.
Send it to her.
She attaches her own lock and sends it back.
You remove your lock and send it back to her.
She removes her lock.
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