Palindromic Days in century

#BRAINSTORM1.1: How many days are there in a century such that the date written in DDMMYY (taking last two digits of the year count, ranges from 00 to 99) is palindromic? Palindromic number or word me...Read more

Palindrome | Easy Coding


Total attempts : 2
Win : 1 by solving

The security system

#BRAINSTORM1.2: There is a security system of an organization that allows only its employees and associates to login with their respective email IDs and a common password. In order to make the passwor...Read more

Combination | permutation | for loop


Total attempts : 2
Win : 1 by solving

Numbers with special property

#BRAINSTORM1.3: How many numbers are there between 1 and 1000 such that the sum of its proper factors (excluding 1 and itself) exceeds the number itself? Example: 20 is such a number because of sum ...Read more

PROPER FACTORS


Total attempts : 2
Win : 1 by solving

Probability based on divisibility

#BRAINSTORM1.4: Find the probability that a 3-digit number xyz will be divisible by all of 2-digit numbers xy, yz and xz. Submit the answer in reduced A/B format...Read more

Probability|Divisibility


Total attempts : 2
Win : 1 by solving

Finding number pairs with same HCF & LCM

#BRAINSTORM1.6: Find the number of pairs of a pair of numbers of at most 2 digits (all the 4 numbers) that exist which have both their HCF and LCM same. Example of such a pair of a pair of numbers is ...Read more

Common HCF, LCM


Total attempts : 2
Win : 1 by solving

Special numbers

#BRAINSTORM1.7: Special numbers exist that such that the number of pairs of digits having the difference between them equal to the number of digits appearing between them in the number, is equal to it...Read more

Speciality|Smallest|Largest


Total attempts : 2
Win : 1 by solving

Textbook page numbering

#BRAINSTORM2.2: A textbook consists of 350 pages with all the pages numbered except the first ten that are reserved for title page, index, acknowledgement, preface and a brief introduction to the cont...Read more

Maximum digit appearance


Total attempts : 2
Win : 1 by solving

Palindromic numbers

#BRAINSTORM2.4: Find the number of n-digit palindromic numbers that exist, as a function of n....Read more

Speciality of numbers|palindromic number counting


Total attempts : 2
Win : 1 by solving

Logical indicative number puzzle

#BRAINSTORM2.3: If 8+3=24 and 8*3=95, then 8-3=?...Read more

Number puzzle|Logical reasoning


Total attempts : 2
Win : 1 by solving

Finding analytical solutions

#BRAINSTORM2.5: For x,y>1, if a solution of x^y=y^x is (h,k), then either h or k lies in the interval (a,b], b having such a value that the interval is only small enough to hold all values of the smal...Read more

Graphical approach|Analytical reasoning|Coordinate geometry


Total attempts : 2
Win : 1 by solving

Finding missing next term in number series

#BRAINSTORM2.6: Find the next term in the series: 2,6,2,3,2,3,2,__....Read more

Number series|Missing term|Next term


Total attempts : 2
Win : 1 by solving

Finding missing term in number series

#BRAINSTORM2.7: Find the missing term in the sequence: 1,2,6,6,3,_,9,9,27,27,36,......Read more

Missing term|Number series


Total attempts : 2
Win : 1 by solving

Finding a certain numbered term in repetitive number sequence

#BRAINSTORM3.1: Find the 100th term of the series: 1,3,3,5,5,5,7,7,7,9,9,9,11,11,11,11,......Read more

Number sequence|Finding a certain numbered term|Repetitive


Total attempts : 2
Win : 1 by solving

Finding last term having a certain number of digits

#BRAINSTORM3.2: Find the last three-digit term in the series: 1,3,7,13,33,58,88,......Read more

Number series|Last term with certain condition


Total attempts : 2
Win : 1 by solving

Position and speed

#BRAINSTORM3.3: There are four persons A,B,C,D standing at the four corners of a square room and another person E standing at the centre of the room. If A has to reach E in a fixed time by covering th...Read more

Speed regulation|position|time to reach and meet


Total attempts : 2
Win : 1 by solving

Sum of missing terms in number series

#BRAINSTORM3.4: Find the sum of the missing terms in the series: 0,4,6,_,12,15,18,21,_,30,.....Read more

Number series|Sum of missing terms


Total attempts : 2
Win : 1 by solving

Polygon mensuration & trigonometry

#BRAINSTORM3.5: The area of an n-sided regular polygon of side length a is given by (na^2/x)tan (180y/n) where the angle 180y/n is in degrees. For what value of n is x=y?...Read more

Mensuration|trigonometry|polygon


Total attempts : 2
Win : 1 by solving

Finding number of rational positive integral solutions

#BRAINSTORM3.6: Find the number of rational positive solutions (x,y) to the equation x^y=4096 such that y is an integer....Read more

Integral solution finding|Exponential


Total attempts : 2
Win : 1 by solving

Finding last two digits

#BRAINSTORM3.7: Find the last two digits in 64^(64!) where ! denotes factorial....Read more

Factorial|Last two digits|Long number


Total attempts : 2
Win : 1 by solving

Minimum expression value finding

#BRAINSTORM4.1: Find the minimum value of n+2x/y (y,n are integers) such that (x+y)^n - (x-y)^n is a multiple of 10 if y is fixed as a non-multiple of 5....Read more

Binomial theorem|Minimum value


Total attempts : 2
Win : 1 by solving

Sum of possible real values

#BRAINSTORM4.2: If (x^k-1)/(x-1)=0 for k=even and positive, then find the sum of possible real values of x^(k/2)....Read more

Complex analysis|Multiple roots|Sum of possible real values of a term raised to a power


Total attempts : 2
Win : 1 by solving

Solving equations containing surds or roots

#BRAINSTORM4.3: If sqrt(x)+sqrt(y)=asqrt(xy) and the value of x+x/y-sqrt(4x^2/y) is unity, then find the value of a....Read more

Equation solving|Square root|Surd


Total attempts : 2
Win : 1 by solving

Function with infinitely recursive arguments

#BRAINSTORM4.4: If f(x) denote the xth root of x, then the sum of the number of solutions and the values of the solutions of the equation f(xf(xf(x...infinite terms...)=x will be?...Read more

Function|Infinitely recursive|Solving for values and number of solutions


Total attempts : 2
Win : 1 by solving

Remainder finding

#BRAINSTORM4.5: Find the remainder when 1+2^2+3^3+...+9^9+10^10 is divided by 11....Read more

Remainder and Divisibility|Multiple terms|Long expression


Total attempts : 2
Win : 1 by solving

Odd term out and its replacement

#BRAINSTORM4.6: Find the sum of the odd term out and the actual term that should replace it: 3,15,145,1649,23401,......Read more

Number sequence|Sum|Finding odd term out with replacement


Total attempts : 2
Win : 1 by solving

Interesting problem on manual operation of 7-segment display

#BRAINSTORM4.7: A 7-segment display is manually worked on using 7 pieces of white paper corresponding to the size of the 7 segments of the display. What is the minimum number of movements of the piece...Read more

7 segment display|Minimum number of operations in manual operations|Miscellaneous


Total attempts : 2
Win : 1 by solving

Spider to cover minimum distance

#BRAINSTORM5.1: A spider is sitting in one of the eight corners of a small cuboidal room of dimensions 5 m×5 m×4 m. What is the minimum distance that the spider has to cover (in m) in returning to t...Read more

Minimum distance coverage|Conditional movement


Total attempts : 2
Win : 1 by solving

Minimum number of moves for knight movement from one corner to other in a chess board

#BRAINSTORM5.2: In the game of chess, a knight is allowed to move two and a half squares in each move,i.e., two squares horizontally and one square vertically or vice versa. On an empty board, what is...Read more

Chess board|Knight|Minimum moves to reach diagonally opposite corner


Total attempts : 2
Win : 1 by solving

Finding the winner in a game of round table seating and rearrangement

#BRAINSTORM5.3: There are n (n=odd) number of people sitting around a round table equidistant from one another serially numbered 1 to n. They start playing a game starting with the person numbered 1 a...Read more

Finding winner in the game|Round table seating|Rearrangement


Total attempts : 2
Win : 1 by solving

Finding number of times a digit group occurs

#BRAINSTORM5.4: For positive integers having upto 4 digits, find the number of times the group 10 occurs. For example: In each of 310 and 3101, the group 10 occurs once....Read more

Digit group occurrence|Permutation|Combination


Total attempts : 2
Win : 1 by solving

Number of possibilities of carrying out a transaction using coins of different denominations

#BRAINSTORM5.5: Find the number of ways in which a transaction of Rs 50 can be made if there is a sufficient supply of identical 1, identical 2 and identical 5 rupee coins....Read more

Coin supply|Combination|Number of ways of carrying out a transaction


Total attempts : 2
Win : 1 by solving

Maximum and minimum number of digits possible

#BRAINSTORM5.6: Find the difference between the maximum and minimum number of digits that X^Y can have, where X is a 15-digit number and Y=10....Read more

Long number|Difference|Minimum and maximum number of digits


Total attempts : 2
Win : 1 by solving

Numbers with special property

#BRAINSTORM5.7: Find the number of N-digit natural numbers which are such that the number obtained by reversing the digits is greater than the number for N=5 (without using any comma while writing the...Read more

Combinatorics|Digit reversal|Special numbers


Total attempts : 2
Win : 1 by solving

Smallest integral value attained by the function

#BRAINSTORM6.1: Find the smallest integral value that the rational function x(x-2)/(x^2+1) can attain for real values of x....Read more

Smallest value|Integral|Rational function


Total attempts : 2
Win : 1 by solving

CORONA letter rearrangements

#BRAINSTORM6.2: Find the number of words that can formed by rearranging the letters of the word CORONA (including itself) such that for each arrangement the no of consonants counted (from left the wor...Read more

CORONA|Conbinatorics|Consonant & Vowel


Total attempts : 2
Win : 1 by solving

Finding numbers co-prime to those formed by digit reversal

#BRAINSTORM6.3: Find the number of 2-digit numbers such that the numbers and those formed by reversing their digits are co-prime to each other....Read more

Co-prime|Digit reversal|Combinatorics


Total attempts : 2
Win : 1 by solving

Percentage area occupied by inscribed square in isosceles triangle

#BRAINSTORM6.4: Find the percentage area occupied by the inscribed square in an isosceles triangle with length of equal sides and base in the ratio 5:6, rounded off to the nearest integer....Read more

Mensuration|Inscribed|Area


Total attempts : 2
Win : 1 by solving

Binary sequences with each bit having similar adjacent bits

#BRAINSTORM6.5: Find the number of 7-bit binary sequences or numbers such that bits at each position of the sequence has at least one similar (not complement) bit adjacent to them. Examples: 1110011 a...Read more

Binary sequences|Combinatorics|Similar adjacent bit


Total attempts : 2
Win : 1 by solving

Maximum area occupied by squares inscribed in a circle

#BRAINSTORM6.6: Find the maximum area in square units that can be occupied in a circle of diameter 20 units by squares of side length 2 units....Read more

Inscribed squares in circle|Maximum area|Mensuration


Total attempts : 2
Win : 1 by solving

Minimum absolute value finding of an expression consisting of greatest integer function

#BRAINSTORM6.7: Find the minimum absolute value of [x]+[500/x] where [ ] denotes the greatest integer function....Read more

Minimum absolute value|Greatest integer function


Total attempts : 2
Win : 1 by solving

Minimum sum of numbers chosen

#BRAINSTORM7.1: Five 2-digit numbers are chosen such that they contain all the digits 0 to 9. Find the minimum sum of such numbers....Read more

Minimum sum|five 2-digit numbers covering all digits 0-9|permutation & combination


Total attempts : 2
Win : 1 by solving

Unique observations with certain numbers

#BRAINSTORM7.3: Find the number of 2-digit numbers which are such that by reversing the digits and adding a digit before the 2 reversed digits, an integral multiple of original number is formed. (exam...Read more

Digit reversal|Integral multiple of original number|Combination


Total attempts : 2
Win : 1 by solving

#BRAINSTORM7.2: Find the number of 2-digit numbers which are such that by reversing the digits and adding a digit before the 2 digits, an integral multiple of original number is formed. (example: 328 ...Read more


Total attempts : 2
Win : 1 by solving

Chess board area problem

#BRAINSTORM7.4: Find the number of rectangles in a standard chess board that occupy at least 50% of the total board area (which consists of squares)....Read more

Standard chess board|Number of rectangles and squares possible|At least 50% coverage of total board


Total attempts : 2
Win : 1 by solving

Choosing 3 digits to form numbers divisible by first 3 prime numbers

#BRAINSTORM7.5: Find the number of ways in which 3 digits, each from 0 to 9 with repetition allowed, can be selected such that the numbers formed in different arrangements by using them are divisible ...Read more

Divisibility by prime numbers|Combination|Repetition allowed


Total attempts : 2
Win : 1 by solving

Card Game

#BRAINSTORM7.6: What is the product of the maximum and minimum number of hands that can be played in the card game of Hearts?...Read more

Card Game


Total attempts : 2
Win : 1 by solving

Rolling of two dice

#BRAINSTORM7.7: In the rolling of two dice, what is the total number of dots on two dice combined that has the highest chance of occurrence?...Read more

Dice rolling|Chance game|Probability


Total attempts : 2
Win : 1 by solving

Finding the last 4 digits of a long number

#BRAINSTORM8.1: Find the last 4 digits in the number 51^150....Read more

Last few digits|Long number|Binomial theorem


Total attempts : 2
Win : 1 by solving

Finding composite non-perfect square factors

#BRAINSTORM8.2: Find the number of factors of 2700 which are composite but not perfect squares....Read more

Factorization|Composite non-perfect square factors|Divisibility


Total attempts : 2
Win : 1 by solving

Pythagorean triplets

#BRAINSTORM8.3: Find the number less than 100 (among 1,2,3,..99) which is the member of the largest number of Pythagorean triplets with integer entries. Ex: 5 is a member of the 2 Pythagorean triplets...Read more

Pythagorean triplets|Right angled triangle and Pythagoras theorem


Total attempts : 2
Win : 1 by solving

Finding smallest sum of side lengths for given area to semi perimeter and side length to area ratio

#BRAINSTORM8.4: If the ratio of values of a side length and area of a triangle be 1:4 and ratio of its area and semi perimeter value be 3:1, find the smallest sum of side lengths of the other two side...Read more

Properties of triangle|Geometry


Total attempts : 2
Win : 1 by solving

Finding smallest number giving non-zero remainder

#BRAINSTORM8.5: Find the smallest positive integer greater than one which gives the same non-zero remainder when divided by each of the numerals 2,3,..,9....Read more

Non-zero remainder given by smallest number|Divisibility


Total attempts : 2
Win : 1 by solving

The clock time puzzle

#BRAINSTORM8.6: In a 12 hour clock let 12:x and 1:y be two instants between 12 and 1 o clock and 1 and 2 o clock respectively when the hour and minute hands are at right angles to each other. If tma...Read more

Clock|Minute and hour hand|Time problem


Total attempts : 2
Win : 1 by solving

Boat rowing under certain conditions

#BRAINSTORM8.7: Two families one consisting of a man of 80 kg, his wife of 60 kg and their children of 30 kg and another family consisting of a man of 75 kg and his wife of 50 kg wish to cross a river...Read more

Miscellaneous puzzle|Boat rowing problem


Total attempts : 2
Win : 1 by solving

Finding maximum sum of numbers with highest product and no digits common

#BRAINSTORM9.1: A and B are two positive integers such that none of the digits are repeated in either A or B or both taken together. If the product AB is maximum, then find the maximum value of sum A+...Read more

No digit repetition|Maximum sum|Number theory


Total attempts : 2
Win : 1 by solving

Equivalent successive discounts

#BRAINSTORM9.2: If a single discount of 30% is equivalent to three successive discounts of x%, y% and z% such that s=x+y+z and t=integer part of s, tmax and tmin be the respective maximum and minimum ...Read more

Successive discounts|Discounting on marked price


Total attempts : 2
Win : 1 by solving

Minimum number of factors whose sum exceed the number

#BRAINSTORM9.3: What is the possible minimum number of factors (which don't include that number) that are needed to be added to get the sum more than the number taken?...Read more

Factors|Sum of factors exceeding number


Total attempts : 2
Win : 1 by solving

Finding smallest number giving non-zero distinct remainder

#BRAINSTORM9.4: Find the smallest positive integer greater than one which gives distinct non-zero remainders when divided by each of the numerals 2,3,..,9...Read more

Non-zero distinct remainder|Divisibility|Remainder theorem


Total attempts : 2
Win : 1 by solving

Integers with no palindromic factors of two or more distinct digits

#BRAINSTORM9.5: Find the number of positive integers which are not more than 1000 and have no palindromic factors that have more than one distinct digits. Note: A palindromic number is one which does...Read more

Special numbers|Non-palindromic factors|Integers


Total attempts : 2
Win : 1 by solving

Minimum sum of digits

BRAINSTORM9.6: If twenty distinct numbers from 1 to 100 (both inclusive) are chosen such that the sum of their digits when added together gives the least value, then find the sum of such twenty number...Read more

Minimum sum of digits|Number puzzle|Number theory


Total attempts : 2
Win : 1 by solving

Number giving largest sum of digits when multiplied by 11

#BRAINSTORM9.7: Considering numbers having upto 5 digits, find the number (integer) that when multiplied by 11 gives a number with the largest sum of digits....Read more

Largest sum of digits|Special number|Property of multiplication by 11


Total attempts : 2
Win : 1 by solving

Special dates in a century

#BRAINSTORM10.1: Find the number of days in a century such that the number representing the date written in DDMMYY format is divisible by 4 and also no two consecutive digits are of the same nature (o...Read more

Calendar dates|Divisibility by 4|Alternate odd and even digits


Total attempts : 2
Win : 1 by solving

Digit reversal of 3-digit number upon certain arithmetic operation

#BRAINSTORM10.2: It is seen that if the sum of two distinct 2-digit numbers is either added to or taken away from a 3-digit number its digits get reversed. How many such 3-digit numbers exist?...Read more

Digit reversal|Number theory|Tricky arithmetic operations


Total attempts : 2
Win : 1 by solving

Largest possible HCF of two 4-digit numbers with common unrepeated digits

#BRAINSTORM10.3: Find the highest possible HCF of two 4-digit numbers having the same digits without any digit repetition but in a different order. Ex: 3024 and 4032 are two such numbers having the HC...Read more

Highest HCF|4-digit numbers|Common unrepeated digits


Total attempts : 2
Win : 1 by solving

Numbers having all combination of digits prime

#BRAINSTORM10.4: Find the number of 3-digit numbers such that all possible numbers that can be formed with the combination of digits as the original number are prime. Ex: 113 and 337 are such numbers ...Read more

Number theory|Combinatorics|3-digit prime numbers


Total attempts : 2
Win : 1 by solving