Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
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Problem I. 362. (December 2014)

I. 362. Let us consider the following configuration of \(\displaystyle L~(\le 6)\) lamps and \(\displaystyle G~(\le 6)\) buttons controlling this system. Each lamp has a counter. The on/off status of the \(\displaystyle i\)th lamp is reversed as soon as its counter reaches the value \(\displaystyle S_{i}\), and in this case, the new value of this counter will be 0. When pressing the \(\displaystyle j\)th button, we always increase the same set of lamp counters by 1. Each lamp is controlled by at least one button, and similarly, each button controls at least one lamp.

The operation of this system is simulated by using a spreadsheet application. In the example, ``lámpa'' is lamp, ``gomb'' is button, and the row ``Alap'' describes the initial state of the system.

The sheet has the following structure (see also the example):

\(\displaystyle \bullet\) the number of lamps and buttons are entered in cells A1 and A2, respectively;

\(\displaystyle \bullet\) in rows 5 and 13, the header row content is displayed in a cell only if the corresponding lamp is present;

\(\displaystyle \bullet\) in column A and beginning with row 6, the header column is displayed in a cell only if the corresponding button is present;

\(\displaystyle \bullet\) the counter values - to change the state of the lamp when this value is reached - are entered in row 4;

\(\displaystyle \bullet\) the relation between the lamps and buttons is entered in the range beginning with cell B6;

\(\displaystyle \bullet\) the initial state of the counters is entered in row 14, and we assume that initially no lamp is on;

\(\displaystyle \bullet\) beginning with cell A15 and upon entering a button number in the same column one by one, the corresponding row should display the status of the counters, and a text message or a background color change should show when the corresponding lamp is on.

When creating your table, you should use conditional formatting and functions to make sure that cell values are displayed only when necessary, and wrong or missing cell values are clearly visible (A1:A2, B4:G4, A15:A114, B6:G11). Your table should handle at least 100 button presses. (We remark that conditional formatting is not a requirement in the matriculation examination.)

In your solution you cannot use any macros, however, an arbitrary number of auxiliary cells may be used to the right of column H.

Your sheet (i362.xlsx, i362.ods,...) containing the simulation, together with a short documentation (i362.txt, i362.pdf) and also describing the name and version number of the spreadsheet application, should be submitted in a compressed file (

(10 pont)

Deadline expired on January 12, 2015.


13 students sent a solution.
10 points:Kovács 246 Benedek, Kovács Balázs Marcell, Radnai Bálint.
9 points:Mócsy Miklós.
8 points:4 students.
7 points:5 students.

Problems in Information Technology of KöMaL, December 2014