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Problems(2)

10 euro bills, coins of 1 euro May Olympiad (Olimpiada de Mayo) 2015 L2 P1

Source:

9/26/2021
Ana and Celia sell various objects and obtain for each object as many euros as objects they sold. The money obtained is made up of some 1010 euro bills and less than 1010 coins of 11 euro . They decide to distribute the money as follows: Ana takes a 1010 euro bill and then Celia, and so on successively until Ana takes the last 1010 euro note, and Celia takes all the 11 euro coins . How many euros more than Celia did Ana take? Give all the possibilities.
[hide=original wording]Ana y Celia venden varios objetos y obtienen por cada objeto tantos euros como objetos vendieron. El dinero obtenido está constituido por algunos billetes de 10 euros y menos de 10 monedas de 1 euro. Deciden repartir el dinero del siguiente modo: Ana toma un billete de 10 euros y después Celia, y así sucesivamente hasta que Ana toma el último billete de 10 euros, y Celia se lleva todas las monedas de 1 euro. ¿Cuántos euros más que Celia se llevó Ana? Dar todas las posibilidades.
number theory
3digit number wanted, 4 hints May Olympiad (Olimpiada de Mayo) 2015 L1 P1

Source:

9/26/2021
The teacher secretly thought of a three-digit SS number. Students A,B,CA, B, C and DD tried to guess, saying, respectively, 541541, 837837, 291291 and 846846. The teacher told them, “Each of you got it right exactly one digit of SS and in the correct position ”. What is the number SS?
number theoryDigits