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CHESS CAN ENCOURAGE INTEREST IN MS EXCEL AND VICE
VERSA
K. Pastor, K. Bártek, D. Nocar
Department of Mathematics, Faculty of Education, Palacký University (CZECH REPUBLIC)
Abstract
Digital technologies play an increasing role in our life, so it is necessary to direct the educational process
more and more towards the development of digital literacy of pupils. As great attention is paid to MS
Excel at primary and secondary schools, it is useful to find new ways to motivate pupils to use this
software.
Since various board games are played by milliards of people worldwide, it is natural to create a link
between board games and MS Excel. We note that board games can significantly develop combinatorial
skills.
The paper is focused on chess because it is one of the oldest and most famous game. Among other
things, the most popular legend of chess history is analyzed. Using MS Excel, we will show how this
legend can be modified to obtain various interesting results.
We carried out research with the aid of a questionnaire to find out the difference between the
preparedness of prospective primary teachers and prospective lower secondary school teachers to
motivate learning MS Excel with the help of chess. The chi-squared test of independence was used.
Keywords: Chess, MS Excel, digital literacy.
1 INTRODUCTION
MS Excel is one of the most widely used digital tools in the world and is therefore taught at primary and
secondary schools. It seems to be useful to find various ways to motivate pupils to study this software.
Since chess is one of the oldest and most famous games, we would like to offer some ways of motivation
to study MS Excel through chess. Using this motivation can, on the other hand, encourage interest in
chess. We note that desk games can significantly develop combinatorial skills. Solving of combinatorial
problems can help students to succeed for example as computer programmers because it fosters deep
reasoning generally.
Mathematics and chess are also closely linked through mathematical chess problems. The
mathematical chess problem is a mathematical problem that is formulated using a chessboard and
chess pieces [1]. Let us recall the eight queens puzzle [2].
The eight queens puzzle is the problem of placing eight chess queens on an
8 × 8
chessboard so that
no two queens attack each other.
The eight queens puzzle was published by chess composer Max Bezzel in 1848. Many famous
mathematicians, as for example Carl Friedrich Gauss, studied this problem and its generalization with
𝑛
queens on an
𝑛 × 𝑛
chessboard. For the sake of completeness, we recall that the eight queens
problem has 92 distinct solutions. If solutions that differ only by the symmetry operations of rotation are
counted as one, the puzzle has 12 solutions. One solution is shown in Figure 1 [2]. Fig. 2 recalls that a
queen moves any number of vacant squares in a horizontal, vertical or diagonal direction [3].
Another class of mathematical chess problems are the chessboard covering problems. Let us recall for
example the mutilated chessboard problem [4]:
Suppose a standard
8 × 8
chessboard has two diagonally opposite corners removed, leaving 62
squares. Is it possible to place 31 dominoes of size
2 × 1
so as to cover all of these squares?
We only note that it is impossible since a domino placed on the chessboard always covers one white
square and one black square, but the chessboard with opposite corners removed has either 30 white
squares and 32 black squares, or 30 black squares and 32 white squares [4].
In our paper, we will show how we can use MS Excel to solve some problems connected with chess. In
Section 2, we will analyze the most popular legend of chess history. Section 3 is devoted to the initial
Proceedings of ICERI2019 Conference
11th-13th November 2019, Seville, Spain
ISBN: 978-84-09-14755-7
7564
estimation of who has superiority on the chessboard. Section 4 shows that MS Excel can also be used
to determine the colour of a selected chessboard field. Finally, in Section 5, we described our research
which aims to find out the difference between the preparedness of prospective elementary teachers and
prospective lower secondary school teachers to motivate learning MS Excel with the help of chess. We
note that chess diagrams in the pictures are created using the web application Chess Diagram Setup
[5].
Figure 1. Eight queens puzzle
Figure 2. Moves of a queen
2 LEGEND OF CHESS HISTORY
We will deal with the wheat and chess problem which appears in different stories about the invention
chess [6]. The wheat and chess problem can be stated in the following way [6]:
If a chessboard were to have wheat placed upon each square such that one grain was placed on the
first square, two on the second, four on the third and so on (doubling the number of grains on each
subsequent square), how many grains of wheat would be on the chessboard at the finish?
In some legends the problem is expressed in terms of rice grains [6]. The beginning of the process is
shown in Fig. 3.
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Figure 3. Wheat and chess problem
The wheat and chess problem can also be solved by means of MS Excel. The solution procedure is
shown in Table 1 (formulas) and Table 2 (numerical values).
Table 1. Wheat and chess problem - formulas
A
B
C
1
chess field
number of grains
sum of grains
2
1
1
1
3
2
=2*B2
=C2+B3
4
3
=2*B3
=C3+B4
5
4
=2*B4
=C4+B5
6
5
=2*B5
=C5+B6
7
6
=2*B6
=C6+B7
8
7
=2*B7
=C7+B8
∙
∙
∙
∙
61
60
=2*B60
=C60+B61
62
61
=2*B61
=C61+B62
63
62
=2*B62
=C62+B63
64
63
=2*B63
=C63+B64
65
64
=2*B64
=C64+B65
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Table 2. Wheat and chess problem - numbers
A
B
C
1
chess field
number of grains
sum of grains
2
1
1
1
3
3
2
2
3
4
3
4
7
5
4
8
15
6
5
16
31
7
6
32
63
8
7
64
127
∙
∙
∙
∙
61
60
576 460 752 303 423 000
1 152 921 504 606 850 000
62
61
1 152 921 504 606 850 000
2 305 843 009 213 690 000
63
62
2 305 843 009 213 690 000
4 611 686 018 427 390 000
64
63
4 611 686 018 427 390 000
9 223 372 036 854 780 000
65
64
9 223 372 036 854 780 000
18 446 744 073 709 600 000
We can see from Table 2 that the total number of grains is more than 18 trillion. In fact, the total number
of grains equals to 18 446 744 073 709 551 615. The difference between the exact number and the
number calculated in MS Excel (see Table 2, last row) is caused by the limit for storing a number in a
cell, which is 15 numbers [7].
The wheat and chess problem can be modified in various ways [6]. For example:
Would you rather have a billion euros or the sum of a euro doubled every day for an October?
3 EVALUATION OF FORCES ON THE CHESSBOARD
The first step for the position assessment on the chessboard is usually the determination of material
strength of each player. It is well known [8] that the approximate value of chess pieces can be measured
according to Table 3.
Table 3. Values of chess pieces
chess piece
value
pawn
1
knight
3
bishop
3
rook
5
queen
9
We will consider the situation on the chessboard given in Fig. 4.
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Figure 4. Material strength
The determination of material strength on the chessboard can be done by MS Excel as it is shown in
Table 4.
Table 4. Material strength in Fig. 4
A
B
C
1
white
black
2
number of pawns
6
6
3
number of knights
0
2
4
number of bishops
1
2
5
number of rooks
2
2
6
number of queens
1
0
7
sum
28
28
In the cell B7, the formula =B2+B3*3+B4*3+B5*5+B6*9 was used and in the cell C7, the formula
=C2+C3*3+C4*3+C5*5+C6*9 was used. Since the sum of the value of white chess pieces (the cell B7)
equals to the sum of the value of black chess pieces (the cell C7), we can say that the position on the
chessboard is in material balance.
Let us emphasize, however, that the actual power of the figures depends on the specific position on the
chessboard.
4 WHITE OR BLACK FIELD
MS Excel can also be used to determine whether a chess field is white or black. It suffices to use
formulas IF and INT, see Table 5. For example, considering the chess field c6, we have m=3, n=6,
3+6=9, and since the integer part of 9/2 equals 4, we obtain 9≠8 and thus the chess field c6 is white
(compare with Fig. 5).
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Table 5. Colour of field
A
B
C
1
row of chess field
column of chess field
colour of field
2
m
n
=IF(A2+B2=2*INT((A2+B2)/2);”Black”;White)
Figure 5. Colour of field c6
5 RESEARCH
We carried out research with the aid of a questionnaire to find out the difference between the
preparedness of prospective elementary teachers and prospective lower secondary school teachers to
motivate learning MS Excel with the help of chess. A total of 68 prospective primary teachers and 36
prospective lower secondary school teachers studying at the Faculty of Education in Olomouc, Czech
Republic, answered the following simple question:
Have you played chess on a computer at least five times in your life?
The obtained results of our research are given in the following table:
Table 6. Playing chess on a computer by students
Type of study
Elementary
Lower secondary
Playing chess on a computer
yes
23
18
no
45
16
We will use the chi-square test of independence to evaluate the previous data.
Null hypothesis: We assume that there is not an association between the type study and playing chess
on a computer.
Alternative hypothesis: We assume that there is an association between the type study and playing
chess on a computer.
Level of significance: 0,05
Using, for example, MS Excel with CHISQ.TEST function, we obtain that a p-value equals about to
0,063. Thus we can refuse the null hypothesis and it means that there is an association between the
type of study and playing chess on a computer. We can say that there is a better chance that prospective
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lower secondary school teachers will use chess to motivate MS Excel learning than prospective primary
teachers.
ACKNOWLEDGEMENTS
The survey was supported by the project “Math Teachers’ Preparedness for Pupils’ Digital Literacy
Development”, Proj. no. IGA_PdF_2019_001, carried out at the Department of Mathematics, Faculty of
Education, Palacký University in Olomouc.
REFERENCES
[1] Wikipedia, Mathematical chess problems, Accessed 2 September 2019. Retrieved from
https://en.wikipedia.org/wiki/Mathematical_chess_problem.
[2] Wikipedia, Eight queens puzzles, Accessed 2 September 2019. Retrieved from
https://en.wikipedia.org/wiki/Eight_queens_puzzle
[3] Wikipedia, Rules of chess, Accessed 2 September 2019. Retrieved from
https://en.wikipedia.org/wiki/Rules_of_chess
[4] Wikipedia, Mutilated chessboard problem, Accessed 2 September 2019. Retrieved from
https://en.wikipedia.org/wiki/Mutilated_chessboard_problem
[5] Chess Diagram Setup, Accessed 2 September 2019. Retrieved from
https://www.jinchess.com/chessboard/composer/
[6] Wikipedia, Wheat and chessboard problem, Accessed 2 September 2019. Retrieved from
https://en.wikipedia.org/wiki/Wheat_and_chessboard_problem
[7] Excel specification and limits, Accessed 2 September 2019. Retrieved from
https://support.office.com/en-us/article/excel-specifications-and-limits-1672b34d-7043-467e-
8e27-269d656771c3
[8] Wikipedia, Chess piece, Accessed 2 September 2019. Retrieved from
https://en.wikipedia.org/wiki/Chess_piece
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