Reasoning
There are 140 days between the two dates, and these 140 days are split in the following way:
4 x Answer | 50 days | Answer
We already know about 50 days, so we have to split the remaining 90 days into the ratio 4:1, which is 72:18.
72 days | 50 days | 18 days
?
Puzzle 6
Can you find the country hidden in the following paragraph?
Welsh horses are my favourite animal. Tapir, llama, marmoset, and elephant closely follow. I don't care much for English rabbits nor ocelots, adders, goldfish, and spaniels.
Welsh horses are my favourite aniMAL. TApir, llama, marmoset, and elephant closely follow. I don't care much for English rabbits nor ocelots, adders, goldfish, and spaniels.
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 2:
You are dealt the Blue King and your friend makes three statements:
My card would beat a Green King. Knowing this, if my card is more likely to be a Jack than a Queen, then my card is actually a King. Otherwise, it isn't. Given all of the information you now know, if my card is more likely to beat yours than not, then my card is Red card. Otherwise, it isn't.
Who has the higher card, you or your friend?
Hint
List all of the cards, and then eliminate some using (1).
Answer
You.
Reasoning
You were dealt the Blue King.
The possible cards, in order, are:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King (your card)
Orange King
Green King
Red Queen
Blue Queen
Orange Queen
Green Queen
Red Jack
Blue Jack
Orange Jack
By (1), your friend's card is higher than the Green King, so your friend can only have one of the following cards:
Green Jack
Red Ace
Blue Ace
Orange Ace
Green Ace
Red King
Blue King (your card)
Orange King
By (2), their card is more likely to be a Jack (1) than a Queen (0), so their card is a King. Leaving:
Red King
Blue King (your card)
Orange King
By (3), only 1 could beat your card, so it is not more likely to beat yours, therefore their card is not Red. Leaving:
Blue King (your card)
Orange King
So your friend must have the Orange King, which your card beats.
Reasoning
Since no digit is duplicated, neither number can end in 1, otherwise, the last digit of the answer would already have been used.
Neither number can end in 5 because the answer would then end in 5 or 0.
So the first number can only be 62, 63, 64, 67, or 68.
We can now look at what the second number can end with, and we find that …
if the first number was 62, the second number can only end in 4 or 7.
Why …
not 1 as previously explained
not 2 because we've already used that in the 62
not 3 because 62 x *3 would end in 6, which is already in the 62
not 5 as previously explained
not 6 because we've already used that in the 62
not 8 because 62 x *8 would end in 6, which is already in the 62
We can repeat this for the other possible first numbers and find that …
if the first number was 62, the second number can only end in 4 or 7.
if the first number was 63, the second number can only end in 4, 7, or 8.
if the first number was 64, the second number can only end in 2, 3, 7, or 8.
if the first number was 67, the second number can only end in 2, 3, or 4.
if the first number was 68, the second number can only end in 3 or 4.
Let's check these in turn …
If the first number was 62, the only possible values are:
62 x 14 = 868
62 x 34 = 2108
62 x 54 = 3348
62 x 74 = 4588
or
62 x 17 = 1054
62 x 37 = 2294
62 x 57 = 3534
62 x 87 = 5394
Only 4 calculations are required for each option, as we didn't need to check 62 x 84 as we already know that the answer would end in 8, or 62 x 47 as we already know that the answer would end in 4.
All of these answers fail as they don't contain all of the digits.
Similarly, we can look at 63, then 64, etc. For each of the numbers, we have to check the possible endings, but in each case, only 4 calculations are required (as seen in the examples above).
