MathDB

1

Part of 2023 May Olympiad

Problems(2)

4 kids and their mothers, hidden chocolate eggs game

Source: 2023 May Olympiad L2 p1

3/24/2024
At Easter Day, 44 children and their mothers participated in a game in which they had to find hidden chocolate eggs. Augustine found 44 eggs, Bruno found 66, Carlos found 99 and Daniel found 1212. Mrs. Gómez found the same number of eggs as her son, Mrs. Junco found twice as many eggs as her son, Mrs. Messi found three times as many eggs as her son, and Mrs. Núñez found five times as many eggs as her son. At the end of the day, they put all the eggs in boxes, with 1818 eggs in each box, and only one egg was left over. Determine who the mother of each child is.
combinatoricsnumber theoryalgebra
sum of digits 1-100 (2023 May Olympiad L1 p1)

Source:

3/24/2024
Juanita wrote the numbers from 11 to 1313 , calculated the sum of all the digits he had written and obtained 1+2+3+4+5+6+7+8+9+(1+0)+(1+1)+(1+2)+(1+3)=55.1+2+3+4+5+6+7+8+9+(1+0)+(1+1)+(1+2)+(1+3)=55. His brother Ariel wrote the numbers from 11 to 100100 and calculated the sum of all the digits written. Find the value of Ariel's sum.
algebranumber theory