Puzzles

Interesting how these puzzles make your mind fresh. Anyways, I am right now in a puzzle solving spree.. So I was searching for some websites with puzzles .. and found an excellent website, where I can learn and think,

http://en.allexperts.com/q/Puzzle-Solving-1841/

Trust me, this is good. I am going to blog down the supporting theorems and techniques for later reference.

Bayes Theorem:

P(A|B) = P(AnB)/P(B)

P(A|B) - conditional probability. Probability of A happening given B has happened.
P(A) & P(B) - prior probability.

Multiplication tricks:

Multiplication of two digit number by 11:
The result will be the first digit, sum of the two digit and the second digit of the given number.
Eg: 4_2 is the two digit number. The result would be 462, where 6 is sum of first (4) & second(2) digit.
Given 4_8, the result would be 528, since when we add 4+8= 12 add 1 to first digit, and follow the rule above.

Multiplication of any number by 5:
*Divide the number by 2
*If there is a remainder, add 5 to the answer. Else, add 0 to the remainder.
Eg: 246 * 5 :
246/2 = 123 (no remainder)
So result would be 1230.

Say, given 235 * 5:
235/2 = 117(there is a remainder)
so result will be 1175.

Division Techniques:

Divisible by 4, 8,16:
Any number is divisible by 4, only if the last 2 digits of the number are divisible by 4. Similarly for 8 and 16, the last 3 and 4 digits should be considered.
Eg:
5632 is divisible by 4, since 32 is divisible by 4.
It is also divisible by 8, since 632 is divisible by 8.
It is also divisible by 16, since 5632 is divisible by 16.

Divisible by 3,9:
A number is divisible by 3 only if the sum of its digit is divisible by 3. Similarly for 9, the sum of digits should be divisible by 9.
Eg:
23541 is divisible by 3, since 2+3+4+5+1 = 15 is divisible by 3.
334242 is divisible by 9, since 3+3+4+2+4+2=18 is divisible by 9.

Divisible by 11:
A number is divisible by 11, only if the difference between the sum of its digit in the odd places and the sum of its digit in the even places are either 0 or a number divisible by 11.
Eg:
4832718 is divisible by 11. Since (8+7+3+4) - (1+2+8) = 22 - 11 = 11 divisible by 11.