Tutorials

The result of the least value of sum of reciprocals, used in Algebra represents an important principle of value sharing.

For two positive real variables $a$ and $b$ for example, if $a+b=1$, the least value of sum of reciprocals of $a$ and $b$ will occur when the value of the sum 1 is shared equally between the two variables. This remarkable equal value sharing principle hold true for any number of variables as well as for any positive sum of the variables...

In an analog clock the minutes hand moves faster than the hour hand and crosses it 22 times in a day, both going round and round over the clock face. In a typical clock problem, we are asked to find the angle between the two clock hands at a specific time...

For most needs of finding square root, if we remember by heart squares and cubes of a few common integers, using quick factorization we can figure out the square roots or cube roots of numbers be it integer or decimal. But occasionally, in a few specific types of arithmetic problems, there is no other option than to actually evaluate the square root of a number following a method specifically tailored for the purpose...

Occasionally the distinctive expression and its inseparable companion fraction of two componendo dividendo variables, both exist in given and target expressions, but in hidden form. With a closer look and component expression substitution, once possibility of using componendo dividendo is revealed, the problem can be solved in mind quickly, faster than any other method. These form another important class of hidden componendo dividendo problems that need uncovering...