## Leave 6

Take 9 from 6, 10 from 9, 50 from 40 and leave 6. How is it possible?

SIX - 9 (IX) = S
9 (IX) - 10 (X) = I
40 (XL) - 50 (L) = X

Take 9 from 6, 10 from 9, 50 from 40 and leave 6. How is it possible?

SIX - 9 (IX) = S
9 (IX) - 10 (X) = I
40 (XL) - 50 (L) = X

Count the number of times the letter "F" appears in the following paragraph:
FAY FRIED FIFTY POUNDS OF
SALTED FISH AND THREE POUNDS
OF DRY FENNEL FOR DINNER FOR
FORTY MEMBERS OF HER FATHER'S FAMILY.

It appears 14 times. Make sure to count the "F"s in the word "OF", which people commonly miss.

You have a sock drawer.
It has 4 black socks, 8 brown socks, 2 white socks and 8 tan socks.
You need to pull out a matching pair of socks in the dark.
There is no light and you couldn't see the socks.
How many socks you should pull out in the dark to get one matching pair of socks?

Five. You have only four different colors of socks. If you pick 5, you can surely get one pair of matching socks.

On the first day they cover one quarter of the total distance.
The next day they cover one quarter of what is left.
The following day they cover two fifths of the remainder and on the fourth day half of the remaining distance.
The group now have 14 miles left, how many miles have they walked?

68.962962 miles

Tarun Asthnaiya go to his office by local train. However nearby train station is quite far from his place and he used to drive his bike to train station daily with an average speed of 60km/hr. One day at halfway point he relized that due to heavy traffic he got late having average speed of just 30km/hr. How fast he must drive for the rest of the way to catch my local train?

The train is just about to leave the station and there is no way Tarun will be able to catch it this time.

I know a number which when multiplied by multiple of 9 i.e 9 18 27 36 45 ... The output consist of number containing only one digit.
Can you identify the number?

12345679
12345679 × 9 = 111111111 (only 1s)
12345679 × 18 = 222222222 (only 2s)
12345679 × 27 = 333333333 (only 3s)
12345679 × 36 = 444444444 (only 4s)
12345679 × 45 = 555555555 (only 5s)

How can you divide a pizza into 8 equal slices using only 3 straight cuts?

Cut 1: Cut the pizza straight down the middle into two halves.
Cut 2: Keeping the two halves in the place, cut the pizza straight down the middle at right angles to the first cut (you will be left with 4 equal quarters)
Cut 3: Pile the 4 quarters on top of each other and cut through the middle of the pile. You will be left with 8 equal slices.

Consider the following explanation for why 1=2:
1. Start out Let y = x
2. Multiply through by x xy = x2
3. Subtract y2 from each side xy - y2 = x2 - y2
4. Factor each side y(x-y) = (x+y)(x-y)
5. Divide both sides by (x-y) y = x+y
6. Divide both sides by y y/y = x/y + y/y
7. And so... 1 = x/y + 1
8. Since x=y, x/y = 1 1 = 1 + 1
8. And so... 1 = 2
How is this possible?

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not followinng basic mathematical rules, we are able to get strange results like these.

A man who lives in Middletown has two girlfriends, one in Northtown and one in Southtown. Trains from the Middletown train station leave for Northtown once every hour. Separate trains from the station also leave for Southtown once every hour. No trains go to both Northtown and Southtown.
Each day he gets to the Middletown train station at a completely random time and gets onto the first train that is going to either Northtown or Southtown, whichever comes first.
After a few months, he realizes that he spends 80% of his days with his girlfriend from Northtown, and only 20% of his days with his girlfriend from Southtown.
How could this be?

The train to Northtown leaves every hour, on the hour (9:00AM, 10:00AM, etc...).
The train to Southtown leaves at 12 after the hour (9:12AM, 10:12AM, etc...).
So there is only a 12/60 (1/5) chance that he will end up on the train to Southtown each day, since he will usually get to the station during the 48 minutes of each hour when the train to Northtown will be the next to come.

A man told his son that he would give him $1000 if he could accomplish the following task. The father gave his son ten envelopes and a thousand dollars, all in one dollar bills. He told his son, "Place the money in the envelopes in such a manner that no matter what number of dollars I ask for, you can give me one or more of the envelopes, containing the exact amount I asked for without having to open any of the envelopes. If you can do this, you will keep the $1000."
When the father asked for a sum of money, the son was able to give him envelopes containing the exact amount of money asked for. How did the son distribute the money among the ten envelopes?

The contents or the ten envelopes (in dollar bills) hould be as follows: $1, 2, 4, 8, 16, 32, 64, 128, 256, 489. The first nine numbers are in geometrical progression, and their sum, deducted from 1,000, gives the contents of the tenth envelope.