Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem I. 239. (April 2010)

I. 239. Five busy waiters are working in a popular restaurant. The manager however suspects that they are spending too much time in the kitchen unnecessarily. To investigate this, the manager puts small radio transmitters on the waiters, so the time instant of each waiter entering into or exiting from the kitchen is recorded. (In the example, ``Be'' is ``into the kitchen'', while ``Ki'' is ``out of''.) We know that initially each waiter stayed outside the kitchen. You should analyse the data obtained, according to the description and examples below by using a spreadsheet application.

[1.] Data from file hazai.txt should be copied into cells beginning with A10, then the sheet should be saved as ,,pincer'' in the default format of your application.

[2.] Text cells A1:C8 should be formatted as in the example, while cells containing numeric data should be filled in with results of the tasks below.

[3.] Cell B2 should contain the total number of entries into the kitchen. (In the example, ,,Összesen'' is ,,Totals'', ,,Alkalom'' is ,,Number of occasions'', ,,Idő'' is ,,Duration'' or ``Time instant'', ``Mindenki a konyhában'' is ``Everybody in the kithcen'', while ``először'' and ``utoljára'' are ``for the first time'' and ``for the last time''.)

[4.] Cell C2 should contain the total time waiters spent in the kitchen.

[5.] Cell A3 should contain the identification number of the transmitter. (In the example, ,,pincér'' is ,,waiter''.)

[6.] Cell B3 should contain the number of entries into the kitchen of waiter specified by cell A3.

[7.] Cell C3 should contain the total time the waiter specified by cell A3 spent in the kitchen. Auxiliary cells to the right of column E can be used for computations.

[8.] The 4th row should contain the ratio between the corresponding data of the waiter specified by cell A3 and the totals. (In the example, ,,Arányában'' is ,,Proportionally''.)

[9.] In column D, beginning with the 11th row, you should specify the number of waiters simultaneously in the kitchen after the entry or exit in the actual row has taken place.

[10.] Cell C6 should contain the number of time intervals with each waiter staying in the kitchen.

[11.] Find the first time instant of the first and last intervals when all waiters were simultaneously in the kitchen. Auxiliary computations can be placed to the right of column E.

[12.] Measurements could have been performed easier by recording only the fact of crossing through the kitchen door, without knowing the direction. In this setting, the direction in column C should have been determined by you. By using data from column B, prove the above statement by determining the missing directional information and placing it into column E. You should apply formulae which can be copied flawlessly in the whole column.

[13.] Create a diagram similar to the example showing the number of waiters in the kitchen versus time, until noon. (In the example, ,,Konyhában'' means ,,In the kitchen''.)

Your spreadsheet (i239.xls, i239.ods, ...) together with a short documentation (i239.txt, i239.pdf, ...) -- also describing the name and version number of the spreadsheet application, further a brief description of your solution -- should be submitted in a compressed file (

(10 pont)

Deadline expired on May 10, 2010.


11 students sent a solution.
10 points:Balla Attila, Barta 111 János, Sagmeister Ádám, Szabó 928 Attila.
9 points:Horváth 135 Loránd, Pap 999 Dávid.
6 points:1 student.
5 points:2 students.
2 points:2 students.

Problems in Information Technology of KöMaL, April 2010