Puzzle 197
What number comes next in this sequence:
15 20 20 6 6 19 19 5 14 {?}
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Hint
The sequence is related to 1, 2, 3, 4.
Answer
20.
Each term's initial letter position in the alphabet:
1 = One = O = 15th letter.
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4 = Four = F = 6th letter.
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20 = Ten = T = 20th letter.
Puzzle 198
Start with a number larger than 0, square it, add 4, double, take away 3, times 4 and finally subtract the original number.
If you were now left with 20, what number did you start with?
Puzzle Copyright © Kevin Stone
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Hint
A little algebra might help.
Answer
1/8.
Reasoning
If we convert the question to algebra, we have:
((n^2 + 4) x 2 – 3) x 4 – n = 20
Expanding the brackets and simplifying gives:
(2n^2 + 8 – 3) x 4 – n = 20
(2n^2 + 5) x 4 – n = 20
8n^2 + 20 – n = 20
8n^2 – n = 0 (*)
8n – 1 = 0
8n = 1
n = 1/8
In the equation marked (*) zero is also a potential solution, but as the question tells us that we "Start with a number larger than 0" we know that n can't be 0, and therefore we can safely divide by n.
Double-Checking
1/8
squared = 1/64
add 4 = 41/64
double = 81/32
take away 3 = 51/32
times 4 = 201/8
subtracting 1/8 gives 20, as required.
Puzzle 199
Greenjack Round #3 - Logic Puzzles
You find yourself playing a game with your friend.
It is played with a deck of only 16 cards, divided into 4 suits:
Red, Blue, Orange, and Green.
There are four cards in each suit:
Ace, King, Queen, and Jack.
All Aces outrank all Kings, which outrank all Queens, which outrank all Jacks, except for the Green Jack, which outranks every other card.
If two cards have the same face value, then Red outranks Blue, which outranks Orange, which outranks Green, again except for the Green Jack, which outranks everything.
Here's how the game is played: you are dealt one card face up, and your friend is dealt one card face down. Your friend then makes some true statements, and you have to work out who has the higher card, you or your friend. It's that simple!
Round 3:
You are dealt the Red Queen and your friend makes three statements:
My card could lose to a Blue card.
Knowing this, if I am more likely to have an Ace or a King than a Queen or a Jack, then I have an Orange card. Otherwise, I don't.
Given all of the information you now know, if I am more likely to have a Jack than an Ace, then I actually have a King. Otherwise, I don't.
Who has the higher card, you or your friend?
Puzzle Copyright © E.J. Shamblen
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Hint
List all of the cards, and then eliminate some using (1).
Answer
Your friend.
Reasoning
You were dealt the Red Queen.
The possible cards, in order, are:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King
Orange King
Green King
Red Queen (your card)
Blue Queen
Orange Queen
Green Queen
Red Jack
Blue Jack
Orange Jack
By (1), their card could lose to a Blue card (the Blue Ace), leaving:
Orange Ace
Green Ace
Red King
Blue King
Orange King
Green King
Red Queen (your card)
Blue Queen
Orange Queen
Green Queen
Red Jack
Blue Jack
Orange Jack
By (2), their card is not more likely to be an Ace or a King (6) than a Queen or a Jack (6), so their card is not Orange, leaving.
Green Ace
Red King
Blue King
Green King
Red Queen (your card)
Blue Queen
Green Queen
Red Jack
Blue Jack
By (3), their card is more likely to be a Jack (2) than an Ace (1), so their card is a King, leaving:
Red King
Blue King
Green King
Red Queen (your card)
All of which beat your Red Queen.
Puzzle 200
Consider an arrow in flight towards a target.
At any given moment of time, a snapshot could be taken of this arrow. In this snapshot, the arrow would not be moving. Let us now take another snapshot, leaving a very small gap of time between them. Again, the arrow is stationary. We can keep taking snapshots for each moment of time, each of which shows the arrow to be stationary. Therefore the overall effect is that the arrow never moves, however it still hits the target!
Where lies the flaw in the logic?
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Hint
This is a puzzle to melt the brain!
Answer
The arrow clearly reaches the target.
This is a classic paradox, attributed to Zeno of Elea, a Greek philosopher from Italy. Great minds over the centuries have pondered this paradox, and the scope of a solution is beyond the space available here. It is not even clear that a solution to the paradox actually exists.
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