Problems

• #20

  Fives and Sevens

  How many 20-digit numbers are there which are formed using only the digits 5 and 7 and divisible by both 5 and 7....

Contributed by Varun Syal


• #32

  Japanese Robo Awesome-O

  Professor Chaos controls the robot Awesome-O by pressing the forward or back button. He presses the forward button $n$ times and the back button $n$ times, one at a time. It returns back to him after ...

Contributed by Mehak Gupta


• #41

  Cartman Loves One Direction

  Find the number of occurrences of the digit $1$ in all natural numbers between $123456789$ to $1234567890$....

Contributed by Nitish Sharma


• #53

  Harry and his Magical Boxes

  There are 7 magical boxes each containing a label depicting a number. The labels of the boxes are given as $5, 2, 7, 8, 7, 4, 6$. Harry Potter goes to each jar once and shouts a spell. When Harry shou...

Contributed by Rajat Jain


• #59

  Ones and Zeros

  Let $S = 2^a + 2^b + 2^c + 2^d + 2^e$ where $a$,$b$,$c$,$d$,$e$ are distinct whole numbers.

  Let $S_{n}$ be the $n^{th}$ number such that for all $i \lt n, S_{i} \lt S_{n}$ and for $i \gt n, S_{i...

Contributed by Vaibhav Daga


• #62

  Magic in Boxland

  A magician lives in a mysterious Boxland that comprises of eight cities and all of them contain 6 magic wands. Each wand has been colored with one of $n$ colors, such that no two wands in the same cit...

Contributed by Sopan Khosla


• #113

  Monica's Candy Fever

  We all know how much Monica loved candies in her childhood. And, her excessive competitiveness is no big secret! There have been various incidents where the Gellars had brought home some candies (say ...

Contributed by Priyanshu Sheth


• #114

  Revenge with Derangement

  Suppose that there are $N$ persons who are numbered $1, 2, ..., N$. Let there be $N$ hats, also numbered $1, 2, ..., N$. We have to find the number of ways in which no one gets the hat having same num...

Contributed by Adarsh Kumar


• #118

  Analyzing Complexity

  Problems with which we often deals in programming requires us to approximate number of iterations that we are going to perform in loops.

  Given below is a simple pseudo code for which you need to tel...

Contributed by Adarsh Kumar


• #127

  Decamping Twice

  Let $S$ be a set where $S$ $=$ {$1,2,3,4,5…...4444444444$} and $P$ be a subset of $S$ such that $x$ $\in$ $P$ but $2x$ $\notin$ $P$. Let $\left | T \right |$ be the total number of elements in the s...

Contributed by Abhinav Kaushal Keshari


• #144

  Circular paradigm

  Let the number of arrangements of 3n identical Type A balls and 3 identical Type B balls in a circle be $F(n)$. Find $F(100000)*F(100001)$....

Contributed by Akshit Kalra


• #158

  Best Hacker in the World

  Foxtrot and Vampire decided to play a game to decide who is a better hacker. They have $n$ tiles in a line out of which $m$ are white rest all are black. Their task is to change all the black tiles wi...

Contributed by Nitish Bansal


• #162

  One Last Game

  During a game of Mafia, after Verma is killed by Mafia in the first round, he starts getting bored and keeps disturbing others in the game. This irritates everyone else and to keep the game interestin...

Contributed by sajal sourav


• #261

  Occupying Houses

  There are 65 houses arranged along a street and numbered from 0 to 64. Initially, only the $0^{th}$ and $64^{th}$ houses are occupied and the rest are empty. Then, one by one 63 buyers come to purchas...

Contributed by Kavish Lodha


• #263

  Subset Intersection

  Let $S$ be a set of size $n$. Let $T_k$ be the set of all ordered k-tuples $(A_1, A_2, A_3, A_4…...A_k)$ where $A_i$ is a subset of $S$, such that $A_1 ∪ A_2 ∪ A_3 ∪ A_4…...A_...

Contributed by Yaswanth Chunduru