Blog 01 [Problem 01, Secondary 2023]:
Find all possible non-negative integer solution \((x,y)\) of the following equation: $$ x! + 2^y = (x+1)! $$
Blog 02 [Problem 03, Higher Secondary 2023]:
For any positive integer \(n\), \(f(n)\) to be the smallest positive integer that does not divide \(n\). For example, \(f(1) = 2, f(6) = 4\). Prove that for any positive integer \(n\), either \(f(f(n))\) or \(f(f(f(n)))\) must be equal to \(2\).
Blog 03 [Problem 01, Secondary 2022]:
Find all solutions for real \(x\): $$ {\left\lfloor x \right\rfloor}^{3} - 7 {\left\lfloor x + \frac{1}{3} \right\rfloor} = -13 $$
Blog 04 [Problem 5, Higher Secondary 2021]:
How many ways can you roll three 20-sided dice such that the sum of the three rolls is exactly 42? Here the order of the rolls matters.
(Note that a 20-sided die is very much like a regular six-sided die other than the fact that it has 20 faces instead of the regular six.)