An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs and one pair of wings. Now we have all 3 kinds and a total of 18 insects in a cage. We have a total of 118 legs and 20 pairs of wings. How many insects do we have of each kind?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not-rounded numerals equals 24.

What three numbers, none of which is zero, give the same result whether they’re added or multiplied?

A 52% bias toss for head using the 51% tail bias coin was done to obtain a fair result.

Can you find how bias is the floor in this case?

Can you think of a smallest +ve number such that if we shuffle the digits of the number, the new number becomes double the original number?

All of Jacob's shoes are red except two.
All of Jacob's shoes are green except two.
All of Jacob's shoes are yellow except two.

How many shoes does Jacob have?

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

What is the largest number you can write with just 3 digits?

If in a car race, the man who came two places in front of the last man finished one ahead of the man who came fifth, how many contestants were there?

A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?