B. Anunt

Petru intra in scara blocului. Citeste un anunt la avizier: “Factura totala pentru incalzire aferenta lunilor noiembrie-decembrie este in valoare de 20 949,5 RON. Defalcarea este realizata in tabel pentru fiecare apartament, conform regulilor indicate:

1. Firmele de la parter platesc in total 10% din suma totala platita de locatari.
2. Apartamentele nelocuite platesc fiecare 10% din suma platita de un apartament locuit.”

Petru are de platit 650 RON. Pentru ca suma i se pare substantiala, reface repede calculele. Blocul are 11 etaje locuibile, in afara parterului unde au sediul firmele care de asemenea participa la plata. Pe fiecare etaj sunt 3 apartamente, cu exceptia ultimului, unde sunt numai 2 apartamente. Dupa realizalea calculelor, Petru confirma ca suma pe care o are de plata este corecta. “Hmm… sunt mai multe apartamente nelocuite decat credeam”, afirma el. ”Asta m-a facut initial sa cred ca trebuie sa platesc mai putin”. Cate apartamente libere (in care locatarii sunt plecati pe perioada celor 2 luni) sunt in blocul lui Petru?

Sursa: problema originală (Ruxandra F. Olimid)

B. Announcement

Peter enters the building. He reads an announcement: "The total heating bill for November-December is RON 20 949,5. The amount for each apartment is decided according to the following rules:

1. The companies on the ground floor pay a total of 10% of the total amount paid by the tenants.
2. Uninhabited apartments pay each 10% of the amount paid by a habited apartment.”

Petru has to pay RON 650. Because the amount seems to be substantial, it quickly redoes calculations. The block has 11 floors, except for the ground floor (where are the companies which also participate to the payment). At each floor there are 3 apartments, except for the last floor, where there are only 2 apartments. After making the computation, Peter confirms that the amount he has to pay is correct. "Hmm ... there are more uninhabited apartments than I thought," he said. "That initially made me think that I have to pay less." How many uninhabited apartments (i.e. appartments for which the tenants are away for the 2 months) are in Petru's building?

Source: original problem (Ruxandra F. Olimid)