Thursday, May 29, 2014

Cryptarithmetic

This  is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters. The goal is to identify the value of each letter. Lets try this game with the popular one.

\begin{matrix}
     &   & \text{S} & \text{E} & \text{N} & \text{D} \\
   + &   & \text{M} & \text{O} & \text{R} & \text{E} \\
 \hline
   = & \text{M} & \text{O} & \text{N} & \text{E} & \text{Y} \\
\end{matrix}

You have to find the value of each letter involved in above equation.( S, E, N, D, M, O, R, Y ).

Remember the rules :
a) Different letters have different value.
b) Same letters must have same value (i.e. M in MORE and M in MONEY has same value)
c) The range of value is 0-9.

Refer to comment section if you want to tally your answer.

Tuesday, May 27, 2014

Crocodile Dilemma Paradox

If a crocodile steals a child and promises its return if the father can correctly guess exactly what the crocodile will do, how should the crocodile respond in the case that the father correctly guesses that the child will not be returned?

Don't think that logic is too simple. Think every possible cases in perspective of crocodile. Think hard. If you cannot find the paradox see the comment to find the reason of paradox.

Thursday, April 24, 2014

Pirate Gold Problem

There are 5 rational pirates, A, B, C, D and E. They find 100 gold coins. They must decide how to distribute them.
The pirates have a strict order of seniority: A is superior to B, who is superior to C, who is superior to D, who is superior to E.
The pirate world's rules of distribution are thus: that the most senior pirate should propose a distribution of coins. The pirates, including the proposer, then vote on whether to accept this distribution. In case of a tie vote the proposer has the casting vote. If not, the proposer is thrown overboard from the pirate ship and dies, and the next most senior pirate makes a new proposal to begin the system again.
Pirates base their decisions on three factors. First of all, each pirate wants to survive. Second, given survival, each pirate wants to maximize the number of gold coins he receives. Third, each pirate would prefer to throw another overboard, if all other results would otherwise be equal. The pirates do not trust each other, and will neither make nor honor any promises between pirates apart from the main proposal.