The Chess Test (Chesst)

Daya Nidhan Singh

2 Hours 30 Minutes

Name: Date:

Instructions:

• This paper is a non-chessboard paper. You are not allowed to use an interactive chessboard,
physical or digital, to assist in your answering.

• With this booklet, you will also be supplied a spare booklet for extra writing space, and empty
chessboards that you can use to further justify your answers. Be clear as to which chessboards
you refer to.

• This test contains 5 sections, each of which consisting of 9 questions. All questions in section 4
are worth 2 marks. In the other sections, the first three questions are worth 1 mark, the next
three are worth 2 marks, and the final three are worth 3 marks.

• Where you have to specify a board layout, symmetric and rotationally symmetric layouts are
considered identical, unless there are cases in which a particular symmetry makes an answer
incorrect (e.g the use of pawns).

• When writing on the boards, denote white pawns, knights, bishops, rooks, queens, and kings by the
letters P,N,B,R,Q and K. To denote black pieces, add an apostrophe afterwards (i.e P’,N’,B’,R’,Q’
and K’).

• There is a glossary of relevant chess terms in the back. It is highly recommended that you read
it before starting; some terms, such as ’pin’, may be further specified to ensure clarity within the
paper.

• In terms of material value, pawns, knights, bishops, rooks, queens, and kings are worth 1, 3, 3, 5,
9 and ∞ respectively

Information:

• This paper consists of 15 pages.

• The total mark for this paper is 90.

Section 1: Warm-Up Chess Problems
In this section, there are 9 ’traditional’ chess problems, all of which are white to move. Make sure to
write down the entire line for all questions and explain your reasoning (if needed).

8
0Zks0a0s
7
L0o0ZqZ0
6
0o0o0Zno
5
Z0ZNo0o0
4
0Z0Z0Z0Z
3
Z0Z0ZPA0
2
POPZ0O0O
1
S0Z0ZRJ0
a b c d e f g h
Best Move

8
0jrZ0Zns
7
o0o0l0o0
6
0oQZpZ0o
5
Z0ZpOpZ0
4
0Z0Z0Z0Z
3
ZPZ0A0Z0
2
PZPZPZBZ
1
ZKZRZ0S0
a b c d e f g h
White to mate (no en passant)

8
RZ0Z0Z0Z
7
o0Z0Z0Z0
6
nZ0Z0Z0Z
5
sNA0Z0Z0
4
0ZPZ0Z0Z
3
Z0Z0Z0Z0
2
0oPJ0Z0Z
1
jrZ0L0Z0
a b c d e f g h
White to pin a black piece to the king
in 3

3
8
0s0Z0Z0j
7
ZRZ0Z0Z0
6
nZ0Z0Z0Z
5
Z0Z0Z0A0
4
0Z0Z0ZNZ
3
Z0Z0Z0Z0
2
0Z0Z0Z0Z
1
ZKZBZ0Z0
a b c d e f g h
Mate in 7

8
0Z0Z0Z0Z
7
o0Z0Z0Z0
6
kZBZ0Z0Z
5
Z0ZNZ0Z0
4
PZ0Z0Z0Z
3
Z0Z0Z0o0
2
0O0Z0ZPo
1
Z0Z0Z0ZK
a b c d e f g h
Mate in 3

8
0ZBZqZ0s
7
ZrZ0ZpJ0
6
0a0ZrZRS
5
Z0Z0Z0A0
4
0Z0Z0ZkZ
3
Z0Z0L0M0
2
0Z0Z0ZQZ
1
Z0Z0Z0Z0
a b c d e f g h
Selfmate in 2

4
8
0ZnsnZ0s
7
ZkZ0l0a0
6
0o0o0o0o
5
oPoPoPoP
4
PZPZPZPZ
3
ZNZ0ZBZ0
2
0Z0ZQZ0Z
1
Z0JRA0ZR
a b c d e f g h
Best move

8
rmbZkZ0s
7
opo0Zpop
6
0Z0Z0Z0Z
5
Z0Z0Z0Z0
4
0Z0ZPZ0Z
3
Z0Z0ZNJP
2
POqZ0ZPZ
1
SNA0ZBZR
a b c d e f g h
Best move

8
0Z0ZrArZ
7
Z0Z0OROp
6
0Z0Z0m0J
5
Z0Z0Z0ZB
4
0Z0o0ZNl
3
Z0oPOkZr
2
0ZPZRORo
1
Z0aBZ0ZB
a b c d e f g h
White to avoid checkmating black

5
Section 2: Close-proximity mates
In this section, you must places pieces on these 3x3 boards (pawns can be on the edges and do not
promote) such that the king is mated (not going to be mated, but already mated by white). Denote
pawns, queens, knights, bishops and rooks with the letters P, Q, N, B and R respectively.

Z0Z Z0Z Z0Z

0j0 0j0 0j0
Z0Z Z0Z Z0Z
1 queen, 1 rook 2 pawns, 2 rooks, 1 bishop 2 pawns, 3 knights, 1 bishop

Z0Z Z0Z Z0Z

0j0 0j0 0j0
Z0Z Z0Z Z0Z
2 pawns, 2 bishops, 1 rook 2 knights, 1 rook, 1 bishop, 1 2 knights, 2 bishops, 1 pawn
pawn
For the last three questions, justify why you have used the specified piece a minimum number of times.

3
Z0Z
2
0j0
1
Z0Z
a b c
1 pawn, minimal knights

3
Z0Z
2
0j0
1
Z0Z
a b c
1 bishop, 1 rook, minimal knights

3
Z0Z Z0Z 3

2
0j0 0j0 2

1
Z0Z Z0Z
a b c
1
a b c
Two solutions with 1 pawn, 1 knight,
minimal bishops

6
Section 3: Limits of the Game
Below are 9 questions about the limits of what can be performed on a chess board, both in game and
out. Assume the latter if unspecified. Note that you can use the blank chessboards in the other booklet,
and label and refer to them to explain your answers.

a) If a king is immobile (that is it has no squares to go to), and on the next move, it is double
checked, is it always mated? Why?

b) If a pawn moves two squares up and reaches a square horizontally adjacent to one of your pawns,
and your pawn is not pinned, is it always legal to perform en passant? Why?

c) Does there exist a board layout whereby all but one choice of promotion immediately stalemates
your opponent (such as, a queen leads to a checkmate, but any other piece means the game is
stalemated)? If so, how is it possible?

d) In a single move, what is the highest (positive) change in material difference (e.g pawn takes pawn
leads to a relative increase in 1 point)? What is the move?

e) In a game, are all castling mate in 1s unnecessary when the mated king isn’t on the bottom rank?
That is, if the opponent’s king isnt on the bottom rank, is there no setup where the only possible
mate in 1 is through castling?

f) How many pieces (of a single colour) can be attacked after just one move (that weren’t attacked
prior to the move)? Explain your answer?

7
g) In a game, what is the smallest material (assuming the king is infinite) value required (i.e restrict-
ing the movement of the king or putting it in check) to checkmate a king (note that the value of
the king not checkmated should not be counted if it does not participate in the mate)? What is
this position?

h) What is the smallest number of captures required to promote all pawns in a game? You may
assume the kings do not accidentally get mated.

i) What is the largest number of checks (not necessarily possible in a game) that can be made on a
single king that is not a checkmate? How many such positions are there that do not use queens or
kings (consider positions in which rook(s) is/are moved along the same rank/file and/or bishop(s)
along the same diagonal to be the same). You may assume that the king is in the same position
on the board, and that rotationally symmetric solutions are distinct (but as usual, vertically sym-
metric solutions are not). All pieces must be checking pieces.

8
Section 4: Impossible Boards
In this section, there are 9 positions; some of these positions impossible to reach in a standard chess
game. Identify which of these are impossible, and explain why. Further identify the ones that are
possible; these do not need explaining. Unlike the other sections, all questions are worth 2 marks here.

8
rZbZka0s
7
opZ0opop
6
0Zpo0m0Z
5
Z0Z0l0A0
4
0OPZ0O0Z
3
O0OBZNO0
2
0Z0O0Z0O
1
SNZQZRJ0
a b c d e f g h

8
rZ0ZkZ0s
7
o0obZ0op
6
0onapZ0m
5
l0Z0ZpZ0
4
0ZBO0A0Z
3
M0O0ZNO0
2
PO0O0O0O
1
S0ZQS0J0
a b c d e f g h

8
rZ0ZkZ0s
7
opo0ZpZp
6
0Z0o0Mpa
5
Z0Z0L0A0
4
BmbZPZ0Z
3
Z0ZPZ0Z0
2
PO0A0OPO
1
Z0ZRZ0J0
a b c d e f g h

9
8
rZ0lkZ0s
7
o0opZpop
6
bonZ0a0Z
5
Z0ZpM0Z0
4
QZBZPA0Z
3
O0M0O0O0
2
PZ0Z0Z0O
1
Z0JRZ0ZR
a b c d e f g h

8
rZbZrakZ
7
Z0m0Z0Zp
6
po0o0ZnZ
5
ZNo0ZQo0
4
PZBZNZ0Z
3
ZPZPZ0O0
2
0ZPZ0Z0O
1
Z0JRZ0ZR
a b c d e f g h

8
rZbl0skZ
7
opZpZpop
6
0Zno0m0Z
5
Z0a0o0A0
4
0Z0ZPZ0Z
3
Z0MPZNZ0
2
POPZ0OPO
1
S0ZQZRJ0
a b c d e f g h

10
8
nZ0Z0Z0Z
7
Z0o0ZpZ0
6
NoPj0O0Z
5
ZPZ0Z0o0
4
0Z0ZQZPZ
3
Z0ZQZ0J0
2
0Z0S0Z0Z
1
Z0Z0Z0Z0
a b c d e f g h

8
0Zks0Z0s
7
Zbo0a0Zp
6
0onZ0opm
5
o0Z0Z0Z0
4
0Z0l0OBZ
3
OBMPZ0O0
2
0OPL0M0O
1
Z0JRZ0ZR
a b c d e f g h

8
rZ0ZkZ0Z
7
Zna0opZp
6
0o0o0ZpZ
5
ZPZrl0L0
4
PZPZbZ0Z
3
Z0APZ0O0
2
0Z0Z0OnZ
1
ZNZRSKZN
a b c d e f g h

11
Section 5: 4 by 4 clue boards
In this section you are tasked to compose positions on these 4 by 4 boards. Each of these positions have
restrictions you need to satisfy. Note that you are not allowed a pawn on the first or last rank, and
that they can promote should they reach the latter. Denote white rooks, pawns, kings, bishops, queens
and knights with the letters r, p, k, b, q and n. The same applies for black pieces; denote the difference
with an apostrophe (i.e r’, p’, k’, b’, q’ and n’)

• This board contains, and only contains, a black

bishop, and a white pawn, knight, queen and

0Z0Z
king.
4
• The knight is covering the white king, and is on
the bottom rank. 3
Z0Z0
• The king is in the process of being skewered
(you may assume in this case that the king can
2
0Z0Z
Z0Z0
still capture the skewering piece) to capture the 1
queen.
a b c d
• Only one square is undefended by white.

• This board contains, and only contains, a black

4
0Z0Z
queen and king, and a white pawn and king.

• Both kings only defend one square in common

3
Z0Z0
• White is stalemated
2
0Z0Z
1
Z0Z0
a b c d

• This board contains, and only contains, 3 pawns

4
0Z0Z
and 1 bishop of any colours, and a king of each
colour
3
Z0Z0
• Both colours are stalemated
2
0Z0Z
1
Z0Z0
a b c d

12
• This board contains, and only contains, a knight
of each colour, a white bishop and a black rook
4
0Z0Z
• The knights are on squares a minimum of 5
(knight) moves from each other
3
Z0Z0
• The white bishop attacks two pieces
2
0Z0Z
• the black rook is attacked by two pieces. 1
Z0Z0
a b c d

• This board contains, and only contains, a rook,

knight, queen, and bishop, all of which attacking
each other in a cycle (i.e A attacks B attacks C
4
0Z0Z
attacks D attacks A). 3
Z0Z0
• All edges of the board have an occupied square

• No piece can see more than any other piece (in-

2
0Z0Z
cluding pieces of their own colour)
1
Z0Z0
a b c d

4
0Z0Z
Z0Z0
• This board contains, and only contains, a white 3
pawn, bishop, knight, rook and queen

• No piece is in the others’ lines of sight. 2

0Z0Z
1
Z0Z0
a b c d

• This board contains, and only contains, a white

4
0Z0Z
rook, 3 pawns, and 2 knights, and a black king 3
Z0Z0
• All squares except that of the black king is de-
fended by a white piece
2
0Z0Z
1
Z0Z0
a b c d

13
• This board contains, and only contains, a rook,

0Z0Z
bishop, knight, pawn, queen and king of each
colour 4

• The board is vertically symmetric. however the

mirror image of one half has the reverse colours
3
Z0Z0
(e.g white knight on a1 means a black knight on
d1)
2
0Z0Z
• The white king is checkmated (the black king is
not) and is not in a corner square.
1
Z0Z0
a b c d

• This board contains, and only contains, a white

4
0Z0Z
pawn and knight, and a king of each colour. 3
Z0Z0
• The black king is to be mated in (a minimum
of) 6 (with white to move first)
2
0Z0Z
1
Z0Z0
a b c d

14
 Glossary
If you are unfamiliar with chess terminology, or would like clarification on terms, below is a glossary of
terms:

Check: A Check is where a king is in a square which a piece of a different colour sees. A player
cannot put themselves in check

Checkmate: When a King is checkmated, it is in check with the added fact that no move can take
the king out of check

Forcing: A move is forced if it is the only legal move possible.

Line: A line is a sequence of moves that can occur. Lines often branch from what’s known as
the ’main line’, which is the most likely sequence of moves to be taken.

Move: A move is where both black and white move a piece. Often ommitted when saying ’mate
in 3 moves’ or similar.

Pin: This is where a piece is in the way of an attack on a piece (usually the king or of something
of higher value to itself) of the same colour. Specifically, if the piece is unable to move
out of the line of attack, regardless if the attack was present, it does not constitute a pin.
This means that if a piece is unable to move out of the pinning diagonal, file or rank,
with or without a pinning piece (e.g through obstructing pieces of the same colour), then
it cannot be pinned.

Reveal A reveal, or ’revealed attack’, is where a piece moves out of the way so that another piece
can see another.

Seen/Sight: If a piece ’sees’ another, or a piece is in its ’sight’, it means that the seen piece is in a
position which is in the seeing piece’s moveset.

Selfmate: A player selfmates themselves by forcing the other to checkmate them.

Skewer: A skewer is an attack whereby a piece is compelled to move (such as a king under check),
revealing an attack on another piece

Stalemate: When a player has no legal move to make, and are not in check they are in stalemate

15