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Find the inverse function f(x)=x+[x].
(No Solution Yet, 1 Comments) Submitted on 2024-04-19 by Danish Ahmed Khan    

Solve the equation

16x3=(11x2+x-1)√(x2-x+1)
(No Solution Yet, 2 Comments) Submitted on 2024-04-18 by Danish Ahmed Khan    

Find six distinct positive integers A, B, C, D, E, F, G satisfying:
 A3 + B3 = C3 + D3 = E3 + F3 = 19G3.
Please submit primitive solutions only, that is, A, B, C, D, E, F, G should not have a common factor.

(No Solution Yet, 2 Comments) Submitted on 2024-04-18 by K Sengupta    

Out of 26 ABC’s letters I have erased 15, leaving only those: a,e,i,j,k,o,q,u,v,x,y.

What were my criteria?

(No Solution Yet, 0 Comments) Submitted on 2024-04-17 by Ady TZIDON    

Difficulty: 4 of 5 Last Four Digits (in Just Math) Rating: 5.00
Consider the sum 1^99 + 2^99 + 3^99 + ... + 99^99.
Finding the last digit of this sum was the task of an old problem Last Digit. With a clever setup finding the last two digits was just as easy.

So I present a higher challenge: find the last four digits. No computer programs!
(No Solution Yet, 1 Comments) Submitted on 2024-04-17 by Brian Smith    

Difficulty: 3 of 5 Red and Yellow (in Probability) Rating: 4.50
A bag contains an unknown number of red balls and yellow balls. When N balls are drawn at random (without replacement) the probability that they are all yellow is 1/2. The number of balls in the bag is the minimum for this to happen.

If the first N balls were all yellow, what is the probability that the next ball drawn is red?

Express the probability as a function of N.

(No Solution Yet, 7 Comments) Submitted on 2024-04-16 by K Sengupta    

Solve the floor equation:

[x]3 + 2x2 = x3 + 2[x]2
(No Solution Yet, 2 Comments) Submitted on 2024-04-16 by Danish Ahmed Khan    

If N is a nonnegative integer, the triangular number T(N)=1+2+3+...+N is given by N(N+1)/2.

Find a prime P such that the sum of the divisors of T(P) is a cube.

****The divisors of a positive integer N includes 1 and N.

(No Solution Yet, 3 Comments) Submitted on 2024-04-15 by K Sengupta    

Difficulty: 3 of 5 Digit Increments 2 (in Numbers) Rating: 5.00
For which digits d, is it possible to add d to every digit of a square and get another square?
For example, adding 3 to each digit of 16 gives 49.However, adding zero to each digit in this manner is NOT permissible.

For which digits d are there infinitely many such squares?

*** Digit sums greater than 9 are not allowed. For example, you could not add 8 to the digits of 81 to get 169.

(Solution Posted, 3 Comments) Submitted on 2024-04-15 by K Sengupta    

Let ABCDE be a convex pentagon such that AB = BC = CD and angle BDE = angle EAC = 30. Find the possible values of angle BEC.
(No Solution Yet, 2 Comments) Submitted on 2024-04-14 by Danish Ahmed Khan    

Difficulty: 3 of 5 Sum of 2 Squares (in Numbers) Rating: 5.00
Let A and B be two different squares of positive integers, A < B, such that the set of base ten digits of A is the same as the set of base ten digits of B.

Find the smallest and largest value of A+B, such that A+B consists of 10 distinct digits.

(Solution Posted, 1 Comments) Submitted on 2024-04-14 by K Sengupta    

Each of x, y and z is a positive integer with gcd(x,y,z)=1

Determine all possible pairs (x,y,z) satisfying this equation:

x3+y3=7z3 where x+y+z < 10^10

(No Solution Yet, 1 Comments) Submitted on 2024-04-13 by K Sengupta    

THESE
FIFTY
HAPPY
GIGAS

The 4x5 matrix above has a certain peculiar feature, which allows you to perform a certain card trick. Although it serves ok as a mnemonic for this trick, it is not a nicely structured sentence, like "NEVER TRUST BLIND DATES" (better, but misses the needed feature).

I ask you to find the essential feature, and then to suggest a nice mnemonic, logically making sense.

(No Solution Yet, 3 Comments) Submitted on 2024-04-13 by Ady TZIDON    

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