Riddles.....

Riddle-1: Crossing the River

A farmer is trying to cross a river. He is taking with him a rabbit, carrots and a fox, and he has a small raft. He can only bring 1 item a time across the river because his raft can only fit either the rabbit, the carrots or the fox. How does he cross the river? (You can assume that the fox does not eat the rabbit if the man is present, you can also assume that the fox and the rabbit are not trying to escape and run away)

Answer: The key to solving this riddle is realizing that you have to take the rabbit over first and the switch the fox with the rabbit.

Step 1: Take the rabbit to the other side

Shore	Other Side
Carrots Fox	Rabbit

Step 2: Go back and get the Fox and switch it with the Rabbit 

**The key here is that the carrots and the rabbit are not being left alone.

Shore	Other Side
Carrots Rabbit (Not left alone)	Fox

Step 3: Take the carrots across

Shore	Other Side
Rabbit	Fox Carrots

Step 4: Go back and get the rabbit

Shore	Other Side
	Rabbit Fox Carrots

Riddle-2: Three Brothers on a Farm

Three brothers live in a farm. They agreed to buy new seeds: Adam and Ben would go and Charlie stayed to protect fields. Ben bought 75 sacks of wheat in the market whereas Adam bought 45 sacks. At home, they split the sacks equally. Charlie had paid 1400 dollars for the wheat. How much dollars did Ben and Adam get of the sum, considering equal split of the sacks?

Answer: Every farmer's part is 1/ 3 (45 + 75) = 40 sacks.

Charlie paid $1400 for 40 sacks, then 1 sack costs $1400 / 40 = $35/ sack.

Adam got $35 * (45 - 40) = 35 * 5 = $175. 

Ben got $35 * (75 - 40) = 35 * 35 = $1225. 

Answer: Ben $1225, Adam $175

Riddle-3: The Insurance Salesman

An insurance salesman walk up to house and knocks on the door. A woman answers, and he asks her how many children she has and how old they are. She says I will give you a hint. If you multiply the 3 children's ages, you get 36. He says this is not enough information. So she gives him a 2^nd hint. If you add up the children's ages, the sum is the number on the house next door. He goes next door and looks at the house number and says this is still not enough information. So she says she'll give him one last hint which is that her oldest of the 3 plays piano.

Hint:

Why would he need to go back to get the last hint after seeing the number on the house next door?

Because the sum of their ages (the number on the house) is ambiguous and could refer to more than 1 trio of factors.

Answer: {2, 2, 9}

If you list out the trio of factors that multiply to 36 and their sums, you get:

1 1 36 = 38

1 2 18 = 21

1 3 12 = 16

1 4 9 = 14

6 6 1 = 13

2 2 9 = 13

2 3 6 = 11

3 3 4 = 10

Since the number on the house next door is not enough information there must be more than 1 factor trio that sums up to it, leaving two possibilities: { 6, 6, 1} , {2, 2, 9} . When she says her 'oldest' you know it cannot be {6, 6, 1} since she would have two 'older' sons not an 'oldest.

Riddle-4: Digit Frequency

Part I: What digit is the most frequent between the numbers 1 and 1,000 (inclusive)? To solve this riddle you don't want to manually do all of the math but rather try to figure out a pattern.

The most common digit is '1.' Can you figure out why? No hints until you try the next riddle because the next riddle is closely tied to this one.

Part II: What digit is the least frequent between the numbers 1 and 1,000?

0 is the least common digit even though 1,000 has three zero’s!

Answers for both parts: 

The digits 0 through 9 all follow the same pattern there is exactly 1 occurrence of each digit for every ten numbers. 

For instance the digit 2 appears once between 10 and 19, at 12. And 2 appears once between, 30 and 39 at 32.

However, each of the digits 1 through 9 also appear in other numbers in the tens and hundreds place

again, let's look at 2 which appears in 20, 21, 22, 23, etc... As well as 200,201, 202,203...

So to figure out how to answer the first riddle you had to see what distinguishes the number 1? Only that we are including 1,000 which would be the first '1' in a new series of ten! 

In other words, the digit 1 only has a single extra occurrence (301 occurrences) compared to 2 or 3 or 9 which each have exactly 300 occurrences.

The reason that zero has the least (BY FAR at only 192 occurrences) is because zero does not have any equivalents to 22, 33, 44, 222, 3333 etc...

Riddle-5:

If 9999 = 4, 8888 = 8, 1816 = 6, 1212 = 0, then 1919 =?

Answer: 4

Look at how many closed areas there are.

9999 has 4 closed areas (the top of the '9')

8888 has 8 closed areas, the top and bottom parts of the 8 and there are no other digits

1816 has 3 closed areas, (top and bottom of 8 and bottom of 6, and it has 2 other digits (3*2=6)

1212 has 0 closed areas, (0*4=0)

1919 has 2 closed areas, (top of 9 and it has 2 other digits (2 * 2 = 4))