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Questions 1 to 10, 3 marks each
1.
The value of 2010 − 20.10 is
(A) 1990.09
(B) 1990.9
(C) 1989.09
(D) 1989.9
(E) 1998.9
2.
If m = 3 and n = −
3
5
, then
m
n
equals
(A) −5
(B) 5
(C) −
9
5
(D) −
5
3
(E) 15
3.
The midpoint of P Q is M (−4, 6). The point Q has coordinates (10, 12). The point
P is
(A) (−18, 0)
(B) (−18, 18)
(C) (−10, 0)
(D) (3,9)
(E) (3,18)
4.
The number 63 is 87.5% of which number?
(A) 45
(B) 70
(C) 72
(D) 74
(E) 75
5.
What percentage of the largest square is covered
by the shaded square?
(A) 6.25%
(B) 10%
(C) 12.5%
(D) 16%
(E) 25%
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ...... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6.
Seven scores 8, 10, 24, 28, 23, 9 and x, have the property that the mean and
median are both x. The value of x is
S 2
7.
The radius of circle P is
2
3
of the radius of circle Q and the radius of circle Q is
3
4
of the radius of circle R.
... ...... ... ...... ... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... .... .... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... .... .... .... ... ... ... ... ... ... ... ... ... ... ... ...... ......... ... ... ... ... ... ... .... .... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... .... ... ... ... ... ... ... ...... ...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... .... .... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
P
Q
R
What fraction of the area of the largest circle R is the shaded area?
(A)
1
3
(B)
5
9
(C)
1
4
(D)
3
16
(E)
5
16
8.
A coin is tossed five times. What is the probability that the result will not be five
tails in a row?
(A)
15
16
(B)
27
32
(C)
4
5
(D)
9
10
(E)
31
32
9.
A rectangle is divided into x rows of y identical squares. Half of them are shaded
to form the border with uniform width of 1 square as shown.
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The sum of x and y could be
(A) 17
(B) 20
(C) 18
(D) 19
(E) 16
10.
When the numbers x
3
, x
2
, x, −x and
√
x are arranged in order from the largest to
Questions 11 to 20, 4 marks each
11.
For all values of x, the expression
7
3x
+ 7
2x
7
2x
+ 7
x
is equal to
(A) 49
(B) 7
2x
(C) 7
(D) 7
x
(E) 1
12.
P QS is a triangle with R lying on QS, with P Q = P S = SR and
6
QRP =
6
QP S.
............ ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
Q
S
P
R
The size of
6
P SR, in degrees, is
(A) 30
(B) 36
(C) 45
(D) 60
(E) 70
13.
If
3a + 4b
2a − 2b
= 5, then
a
2
+ 2b
2
ab
equals
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
14.
The value of (123456785) × (123456782) − (123456783) × (123456784) is
(A) −2
(B) −1
(C) 0
(D) 1
(E) none of these
15.
The length of each side of a triangle like the one below is a different prime number
and its perimeter is also a prime number.
... .
What is the smallest possible perimeter of such a triangle?
S 4
16.
The 5-digit number a986b, where a is the first digit and b is the units digit, is
divisible by 72. What is the value of a + b?
(A) 9
(B) 10
(C) 12
(D) 13
(E) 15
17.
A cap consists of six pieces, all the same size and shape.
... ...... ... ...... ...... ... ... ... ... ... ... ... ... ... .... .... .... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... .... .... ... ... ... ... ...
•
... ... ... ...... ...... ...... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... .... ... ... ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ...... ...If each piece can be either gold or brown, how many different caps can be made?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20
18.
For all positive integers n, Snap(n) = 2n if n is even and Snap(n) = 3n if n is odd.
If p is a prime number greater than 2, what is the value of Snap
≥
Snap(p − 1) − p
¥
?
(A) p − 2
(B) 2p − 2
(C) 2(p − 2)
(D) 3p − 2
(E) 3(p − 2)
19.
A circle is inscribed in a quadrant of a larger circle. The
ratio of the area of the inner circle to that of the quadrant
is
(A) 2 : 3
(B) 4 : 5
(C) 3 : (2 +
√
3)
(D)
√
2 :
√
3
(E) 4 : (3 + 2
√
2)
.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... .... .... ... ... ... ... ... ... ... ... ...... ... ...... ... ...... ......... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... .... ... ... ... ... ...... ......20.
The operation
N
means a
N
b = a + b
2
. If a > 0 and (a
N
a)
N
a = a
N
(a
N
a),
then a equals
Questions 21 to 25, 5 marks each
21.
The super factorial number 1! × 2! × 3! × · · · × 12! can be written as a factorial
times a perfect square, that is, in the form m! × n
2
. What is the value of m?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
22.
The rectangular piece of paper pictured has length AB = 24 cm and width
AD = 10 cm. It is folded along the diagonal AC and then triangle ACD is folded
along the line AE so that AD is aligned with AC.
... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ... . ... ... ... ... ...
✿
... ...... ...... ...... ...... ...A
B
D
C
10 cm
24 cm
=⇒
...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... .... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ... ... ... ...... ...... ...... ...... ...... ...... ... ... ... .... ... ... ... ... .✇
... ...A
B
D
C
E
=⇒
...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... .... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. . ...... ...... ...... ...... ...... ... ... ...... ... ... ... ...A
B
D
C
E
=⇒
... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... ... ... ...... ...... ...... ...... ... ...... ...... ...... ...... ....A
B
D
E
C
How long, in centimetres, is DE?
(A)
13
2
(B)
10
√
3
(C)
20
3
(D) 8
(E) 12
23.
There are sixteen different ways of writing four-digit strings using 1s and 0s. Three
of these strings are 1010, 0100 and 1001. These three can be found as substrings
of 101001. There is a string of nineteen 1s and 0s which contains all sixteen strings
of length 4 exactly once. If this string starts with 1111, the last four digits are
(A) 1110
(B) 0000
(C) 0110
(D) 1010
(E) 0111
24.
What is the smallest n such that no matter how n points are placed inside or on
the surface of a cube of side length 16 units, there are at least two of these points
which are closer than 14 units to each other?
S 6
25.
Loki stands at the centre of a forest which has trees with trunks of identical radii
at every integer coordinate point except the origin, where he is standing. From
where he is, he cannot see beyond the second tree in any direction. That is, he
cannot see any tree with either coordinate of magnitude greater than 2. What is
the smallest possible radius of the tree trunks?
(A)
1
2
(B)
1
3
(C)
1
√
10
(D)
1
√
13
(E)
1
2(
√
13 − 3)
For questions 26 to 30, shade the answer as an integer from 0 to 999 in
the space provided on the answer sheet.
Question 26 is 6 marks, question 27 is 7 marks, question 28 is 8 marks,
question 29 is 9 marks and question 30 is 10 marks.
26.
If m + n = 11 and m
2
+ n
2
= 99, what is the value of m
3
+ n
3
?
27.
A 3-digit number is subtracted from a 4-digit number and the result is a 3-digit
number.
−
=
The 10 digits are all different.
What is the smallest possible result?
28.
In the triangle P QR, P Q = P R = 40 cm and S is a point on QR such that
P S = 25 cm. The extension of P S meets the circle through P QR at T .
... ...... ... ...... ...... ...... ... ... ... ... ... ... ... ... ... ... ... ... ... .... .... .... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ... ... ... ... ... ... ... .... .... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ...... ...... ...... ...... ... ... ... ... ... ... ... ... ... ... ...
