Twice ten are six of us,

Six are but three of us,

Nine are but four of us;

What can we possibly be?

Would you know more of us?

Twelve are but six of us,

Five are but four, do you see?

What are we?

Thomas has missed an excessive number of days of school, so he must meet with Principal Davis. Mr. Davis asks him "Why on Earth have you missed so many days?" Thomas replies "There just isn't enough time for school. I need 8 hours of sleep a day, which adds up to about 122 days a year. Weekends off is 104 days a year. Summer vacation is about 60 days. If I spend about an hour on each meal, that's 3 hours a day or 45 days a year. I need at least 2 hours of exercise and relaxation time each day to stay physically and mentally fit, adding another 30 days. Add all of that up and you get about 361 days. That only leaves 4 days for school." The principal knows Thomas is full of it, but can't figure out why. Where is Thomas going wrong?

What is next number in the pattern below:

131 517 192 123 ?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

As we know that white starts the game of chess. Can you find the scenario shown in the picture below is possible when all the white pieces are at the original place while the black pawn is not as in the below picture?

Rob is taller than Edwin, and Jurgen is shorter than Rob.
Of only one of the following statements, we now certainly know it is correct:

A.Edwin is taller than Jurgen
B.Jurgen is taller than Edwin
C.It cannot be determined if Jurgen or Edwin is the tallest.

John Went to the nearby store in a Mall to buy something for her home. Below is the conversation between the two:

John: How much for the one?
Shopkeeper: It is $2
John: How much for the Eleven?
Shopkeeper: It is $4
John: How much for the Hundred?
Shopkeeper: It is $6.

What is John buying?

Rearrange the letters in "new door" to make one word.

Name the three-letter word that can complete the below words:

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10