Question 97
Three friends color the positive integers from $1$ to $2025$ as follows: Alexia colors in red the numbers $1$ and $2$, then Bianca colors in yellow the numbers $3$, $4$ and $5$, and Cristina colors in blue the numbers $6$, $7$, $8$ and $9$. Afterwards, the operation is repeated: Alexia colors in red the next two numbers, Bianca colors in yellow the next three numbers, and Cristina colors in blue the next four. The friends keep on painting, until all the numbers are colored.
a) What will be the color of $2024$?
b) Find the smallest natural number $n$ so that, after $n$ numbers have been colored, the sum of the numbers in yellow is larger than $2024$.
a) What will be the color of $2024$?
b) Find the smallest natural number $n$ so that, after $n$ numbers have been colored, the sum of the numbers in yellow is larger than $2024$.