Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

If 21x = 79x, what is the value of x?

Can you find the ages of a son, father and grandfather based on the following facts?
The sum of the ages of grandfather, father and son is 140 years.
The age of the son in months is the same as the grandfather in years.
The age of the son in days is the same as the father in weeks.

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 is the value of 1/2 of 2/3 of 3/4 of 4/5 of 5/6 of 6/7 of 7/8 of 8/9 of 9/10 of 1000?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

What's a single-digit number with no value?

There is a straight highway. Four different villages lie on that highway. The distance between them is different. The third village is 60km away from the first village; the fourth is 40 km away from the second; the third is 10 km near to the fourth that it is to the second.

Can you calculate the distance between the fourth and the first village ?