Recent questions tagged cmi2015

Let $\Sigma=\{a,b\}.$ Given a language $L\underline\subset \Sigma^{\ast}$ and a word $w\in\Sigma^{\ast}$, define the languages:$$Extend(L,w) :=\{xw\:|\:x\in L\}$$ $$Shrin...

There is a thin, long and hollow fibre with a virus in the centre. The virus occasionally becomes active and secretes some side products. The fibre is so thin that new si...

Consider the code below, defining the functions $f$ and $g$:f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n ...

Consider the code below, defining the functions $f$ and $g$:f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n ...

Consider the code below, defining the functions $f$ and $g$:f(m, n) { if (m == 0) return n; else { q = m div 10; r = m mod 10; return f(q, 10*n + r); } } g(m, n) { if (n ...

An airline runs flights between several cities of the world. Every flight connects two cities. A millionaire wants to travel from Chennai to Timbuktu by changing at most ...

A cook has a kitchen at the top of a hill, where she can prepare rotis. Each roti costs one rupee to prepare. She can sell rotis for two rupees a piece at a stall down th...

A cook has a kitchen at the top of a hill, where she can prepare rotis. Each roti costs one rupee to prepare. She can sell rotis for two rupees a piece at a stall down th...

Consider a social network with $n$ persons. Two persons $A$ and $B$ are said to be connected if either they are friends or they are related through a sequence of friends:...

The school athletics coach has to choose $4$ students for the relay team. He calculates that there are $3876$ ways of choosing the team if the order in which the runners ...

A college prepares its timetable by grouping courses in slots A, B, C, . . . All courses in a slot meet at the same time, and courses in different slots have disjoint tim...

Twin primes are pairs of numbers $p$ and $p+2$ such that both are primes—for instance, $5$ and $7$, $11$ and $13$, $41$ and $43$. The Twin Prime Conjecture says that ther...