Using a Maple Program written by Doron Zeilberger .
Dedcicated to Doron's aunt Brigitte Weiss on her 90th brithday and to the memory of Doron's uncle Hans Weiss (1902-1983).
This is Chapter III of the webbook Computer-Generated Alphametic.
This chapter consists of 150 alphametic problems each consisting of a 3-digit by 2-digit long multiplication problems. You have to find the numbers. The solutions are at the end.
PROBLEMS
1.
O D E
x
D O
____________________
D E A L
B O A T
____________________________
L E G A L
2.
O U R
x
O R
____________________
E D I T
T E A R
____________________________
T R U S T
3.
C R Y
x
E T
____________________
R A T A
P I C A
____________________________
P L A Z A
4.
E G G
x
R E
____________________
A R I D
B E A R
____________________________
B R O O D
5.
I N K
x
T I
____________________
D U T Y
A M M O
____________________________
T O A D Y
6.
S A D
x
S A
____________________
S O D A
P A S S
____________________________
O M E G A
7.
S K I
x
S O
____________________
M E T E
T S A R
____________________________
T A S T E
8.
I L L
x
E L
____________________
T O N E
L I E N
____________________________
I R A T E
9.
P S I
x
I I
____________________
M E S A
M E S A
____________________________
M A G N A
10.
B E Y
x
B E
____________________
A L L Y
T E A T
____________________________
B Y W A Y
11.
L E T
x
T O
____________________
S H O E
S O W N
____________________________
A P P L E
12.
R E P
x
I I
____________________
B R A N
B R A N
____________________________
P A E A N
13.
E R R
x
L A
____________________
B L A T
R O O D
____________________________
R A B A T
14.
F R Y
x
I F
____________________
A F A R
T R A Y
____________________________
T A P I R
15.
E F T
x
P A
____________________
C O C A
S T O P
____________________________
S E P I A
16.
T O T
x
I x
____________________
O x E N
L A S E
____________________________
L I N E N
17.
A R M
x
A H
____________________
D I R E
T E N D
____________________________
T H R E E
18.
T I P
x
E M
____________________
T O I L
P L A T
____________________________
T O N A L
19.
H E N
x
A N
____________________
T E x T
T H I S
____________________________
T A I N T
20.
H O E
x
H A
____________________
W H O A
A V O W
____________________________
A L P H A
21.
R E T
x
N O
____________________
M E S S
T O S S
____________________________
T R E S S
22.
E T A
x
A S
____________________
G A L L
S L A T
____________________________
P U P A L
23.
E V E
x
E T
____________________
S O R A
R A T A
____________________________
V I L L A
24.
T I N
x
N E
____________________
S P E C
I N T O
____________________________
I O N I C
25.
T I E
x
I S
____________________
R U S E
N E A P
____________________________
N O O S E
26.
A N A
x
N E
____________________
N I N E
D I A L
____________________________
N O I S E
27.
L Y E
x
L A
____________________
E N V Y
T O N E
____________________________
T A T T Y
28.
T O T
x
T I
____________________
L A N E
L O S T
____________________________
A L G A E
29.
O L D
x
I I
____________________
L E N S
L E N S
____________________________
L O E S S
30.
O A F
x
I I
____________________
W R I T
W R I T
____________________________
A W A I T
31.
E G O
x
E N
____________________
R A I N
R O A D
____________________________
P A G A N
32.
E T A
x
E N
____________________
T A N H
T H E Y
____________________________
T O O T H
33.
O V A
x
B Y
____________________
N A R Y
E N O L
____________________________
E V E R Y
34.
S K I
x
I S
____________________
T H A T
H I K E
____________________________
T A I N T
35.
A W N
x
S A
____________________
P O P E
O P E N
____________________________
A D A G E
36.
T O P
x
U P
____________________
E V E N
E A R L
____________________________
P R E E N
37.
Y O N
x
A D
____________________
T A T E
E Y E D
____________________________
G O O S E
38.
P I E
x
E M
____________________
A U T O
T U N A
____________________________
T A N G O
39.
N I T
x
N U
____________________
I D L E
D U A L
____________________________
D E L V E
40.
B O P
x
P A
____________________
I O T A
A K I N
____________________________
K O A L A
41.
T H E
x
S A
____________________
H I R E
P O G O
____________________________
S P I T E
42.
A G O
x
L O
____________________
H O B O
G A L L
____________________________
G U A N O
43.
S E E
x
A D
____________________
R A P T
S T A G
____________________________
S P E N T
44.
D R Y
x
H O
____________________
R O A D
A U N T
____________________________
A H E A D
45.
C U R
x
Y E
____________________
T A P E
A R T Y
____________________________
A C U T E
46.
E G O
x
O N
____________________
S T E W
T R E E
____________________________
T H R O W
47.
T O E
x
I T
____________________
P R O M
P E E R
____________________________
S P A S M
48.
O U T
x
T O
____________________
R A T E
A R U M
____________________________
O B E S E
49.
R H O
x
A H
____________________
B E A D
P L E A
____________________________
P R O U D
50.
P E E
x
H E
____________________
P L E A
O M E N
____________________________
H A L M A
51.
H O E
x
A N
____________________
D E B T
T A P A
____________________________
A R H A T
52.
A L P
x
S O
____________________
C L A P
E A S T
____________________________
S C R A P
53.
T E A
x
N O
____________________
P I E R
O N C E
____________________________
O R D E R
54.
A N T
x
I I
____________________
T E E N
T E E N
____________________________
S T E R N
55.
P I P
x
H A
____________________
S E R A
P O N T
____________________________
P A S H A
56.
Q U A
x
O N
____________________
P L O D
R A T A
____________________________
R O U N D
57.
P L Y
x
R E
____________________
L E E R
Y U L E
____________________________
S A T Y R
58.
S E T
x
P A
____________________
E L S E
A M E N
____________________________
A B A S E
59.
R U E
x
E N
____________________
C O C A
F O R T
____________________________
F A U N A
60.
O A F
x
E T
____________________
R A R E
G A I T
____________________________
G R I P E
61.
T H E
x
E N
____________________
T O I L
G A L A
____________________________
T I D A L
62.
E F T
x
U P
____________________
E A S E
T U F F
____________________________
S T O N E
63.
L E A
x
O W
____________________
C L U E
A C R E
____________________________
A W A R E
64.
R E P
x
E L
____________________
B E T H
S A L T
____________________________
S T A S H
65.
A P E
x
E T
____________________
H A L O
M A S H
____________________________
M O T T O
66.
M U G
x
R E
____________________
A U R A
L U G E
____________________________
M A G M A
67.
G A S
x
M E
____________________
M O R E
S T A R
____________________________
M A T T E
68.
A P E
x
N E
____________________
B O N Y
T E E T
____________________________
T A R D Y
69.
A D O
x
N E
____________________
T I N E
T A P A
____________________________
E L A T E
70.
B O A
x
I I
____________________
A R E A
A R E A
____________________________
P A M P A
71.
A R E
x
E T
____________________
D E A D
B A T T
____________________________
G O U R D
72.
L A B
x
I I
____________________
B I A S
B I A S
____________________________
B L I S S
73.
E N D
x
M E
____________________
D E J A
D A M P
____________________________
D R A M A
74.
P P M
x
H E
____________________
R A P E
S H A H
____________________________
P U R S E
75.
E T C
x
E M
____________________
T U B A
T E N T
____________________________
M A N N A
76.
A R T
x
A T
____________________
S L O E
M E S A
____________________________
T H R E E
77.
Z I P
x
N E
____________________
O O Z E
S P A N
____________________________
S I E G E
78.
S I N
x
I T
____________________
N E S T
S A N D
____________________________
S T U N T
79.
T W O
x
I I
____________________
B I T E
B I T E
____________________________
B O W I E
80.
Q U O
x
R E
____________________
T A U T
T H O U
____________________________
T R E A T
81.
R I B
x
H E
____________________
U R E A
A B B E
____________________________
A L O H A
82.
P E T
x
A T
____________________
B O N A
P R E Y
____________________________
P L A Y A
83.
G N U
x
U P
____________________
N I C E
P I E R
____________________________
P R O N E
84.
E W E
x
I T
____________________
P A L E
T E A R
____________________________
T A B L E
85.
O D D
x
I I
____________________
D E A N
D E A N
____________________________
D I V A N
86.
N I B
x
N E
____________________
T A L E
T O O L
____________________________
A P P L E
87.
O W E
x
B E
____________________
B O S S
A B U T
____________________________
S W I S S
88.
E F T
x
D U
____________________
R A T E
R O O D
____________________________
R U P E E
89.
D A Y
x
A N
____________________
E D I T
T R E E
____________________________
A B B O T
90.
E G O
x
E N
____________________
M I T E
S A N S
____________________________
M O O S E
91.
P E A
x
I N
____________________
O I L Y
T Y P O
____________________________
T A T T Y
92.
G A S
x
I I
____________________
A M E N
A M E N
____________________________
A S P E N
93.
R U E
x
E T
____________________
O G L E
L U G E
____________________________
L O O S E
94.
E E L
x
E M
____________________
C E N T
M E L D
____________________________
E C L A T
95.
U S E
x
E L
____________________
S L I T
T A I L
____________________________
S T I N T
96.
R E D
x
I I
____________________
G O A T
G O A T
____________________________
I D I O T
97.
O W L
x
T I
____________________
R O L L
I O T A
____________________________
T R I L L
98.
R E P
x
P A
____________________
T S A R
S O U P
____________________________
S A T Y R
99.
A R M
x
I I
____________________
L A V A
L A V A
____________________________
L E M M A
100.
S P A
x
P I
____________________
L O L L
D R O P
____________________________
P E A R L
101.
E L L
x
B E
____________________
B U L B
R O L E
____________________________
C R U M B
102.
A R E
x
A T
____________________
D Y N E
Y A W N
____________________________
D R O N E
103.
R H O
x
P I
____________________
T H A T
T R A P
____________________________
T O A S T
104.
N A G
x
N U
____________________
T A P E
A U N T
____________________________
A C U T E
105.
E R G
x
A T
____________________
G A I N
T A N G
____________________________
A N I O N
106.
O I L
x
I I
____________________
S T A Y
S T A Y
____________________________
I N L A Y
107.
N E E
x
N O
____________________
T O R E
T A I L
____________________________
T H E R E
108.
P I P
x
O N
____________________
A C M E
C O D A
____________________________
A M P L E
109.
A P E
x
E N
____________________
P R A M
T A P A
____________________________
T O T E M
110.
A N A
x
A M
____________________
S E N D
T R O Y
____________________________
S T E E D
111.
P O I
x
I V
____________________
T O T E
S E A T
____________________________
S I E V E
112.
U R N
x
U S
____________________
O P E N
D E E R
____________________________
O L D E N
113.
N O N
x
E T
____________________
D A T E
R E A P
____________________________
P L A C E
114.
S E N
x
E M
____________________
A T O M
S A N E
____________________________
S P A S M
115.
A L E
x
I I
____________________
L E S S
L E S S
____________________________
L O E S S
116.
E W E
x
W E
____________________
W A T T
D I V E
____________________________
D A V I T
117.
I L L
x
L O
____________________
T O R N
O R A L
____________________________
O C E A N
118.
L A W
x
I S
____________________
T W I T
S O L O
____________________________
S W E E T
119.
E R R
x
M E
____________________
C A L M
C O C A
____________________________
D R E A M
120.
L U G
x
T O
____________________
T U B A
A B L E
____________________________
A L O H A
121.
R A P
x
E T
____________________
P A S T
B R A E
____________________________
B E S E T
122.
T E E
x
E L
____________________
P L A Y
B R A E
____________________________
B A L D Y
123.
P P M
x
I I
____________________
A W A Y
A W A Y
____________________________
A P P L Y
124.
E T A
x
D O
____________________
T I N Y
O O Z E
____________________________
E N T R Y
125.
H U T
x
I I
____________________
T H A T
T H A T
____________________________
T A U N T
126.
O P T
x
N E
____________________
N A P E
P L A N
____________________________
P H A G E
127.
A N T
x
R E
____________________
B O N Y
T U B E
____________________________
T A T T Y
128.
A W L
x
E L
____________________
P A I L
P O G O
____________________________
P U P I L
129.
A G E
x
A D
____________________
O R G Y
T A R A
____________________________
E N T R Y
130.
G A S
x
B Y
____________________
S C A T
S H A H
____________________________
Y A C H T
131.
P I E
x
P A
____________________
E D G Y
T O N G
____________________________
T A T T Y
132.
A G O
x
N O
____________________
T I D E
D E J A
____________________________
E L I T E
133.
N E E
x
B E
____________________
P U T T
A R E A
____________________________
A D A P T
134.
B E E
x
U P
____________________
C O C K
C L U B
____________________________
B R O O K
135.
A D O
x
V I
____________________
M U L E
M A I M
____________________________
A L I V E
136.
A L B
x
I T
____________________
B I T E
E T C H
____________________________
E E R I E
137.
F L Y
x
Y E
____________________
A S H Y
S L A Y
____________________________
S A P P Y
138.
T A O
x
E N
____________________
A C R E
C O N N
____________________________
N U R S E
139.
I M P
x
T I
____________________
G A M E
A T O M
____________________________
G R A T E
140.
A P E
x
S A
____________________
L I L T
A T O P
____________________________
A W A I T
141.
V I I
x
S A
____________________
V E A L
P A T E
____________________________
T O T A L
142.
I O N
x
I I
____________________
D E U S
D E U S
____________________________
L O E S S
143.
E F T
x
I I
____________________
O O Z E
O O Z E
____________________________
E R A S E
144.
M I x
x
M U
____________________
I S L E
A x E S
____________________________
A B A S E
145.
E N D
x
T O
____________________
D A L E
M I L A
____________________________
M A T T E
146.
T O T
x
E T
____________________
K N E E
S A G A
____________________________
S L A K E
147.
T E N
x
N E
____________________
R O P E
C E L L
____________________________
C L O N E
148.
E R A
x
A D
____________________
R O S Y
W A R T
____________________________
W E E D Y
149.
H E R
x
I I
____________________
A R E A
A R E A
____________________________
P A M P A
150.
S P A
x
P I
____________________
B L I P
L A V A
____________________________
B E B O P
SOLUTIONS
1.
7 5 2
x
5 7
____________________
5 2 6 4
3 7 6 0
____________________________
4 2 8 6 6
2.
6 9 2
x
6 2
____________________
1 3 8 4
4 1 5 2
____________________________
4 2 9 0 0
3.
9 1 4
x
7 2
____________________
1 8 2 8
6 3 9 8
____________________________
6 5 8 0 0
4.
5 6 6
x
8 5
____________________
2 8 3 0
4 5 2 8
____________________________
4 8 1 1 1
5.
9 0 7
x
6 9
____________________
8 1 6 3
5 4 4 2
____________________________
6 2 5 8 8
6.
5 9 1
x
5 9
____________________
5 3 1 9
2 9 5 5
____________________________
3 4 8 6 6
7.
5 1 8
x
5 7
____________________
3 6 2 6
2 5 9 0
____________________________
2 9 5 2 2
8.
8 7 7
x
9 7
____________________
6 1 3 9
7 8 9 3
____________________________
8 5 0 6 6
9.
5 1 7
x
7 7
____________________
3 6 1 9
3 6 1 9
____________________________
3 9 8 0 0
10.
9 6 2
x
9 6
____________________
5 7 7 2
8 6 5 8
____________________________
9 2 3 5 5
11.
5 2 7
x
7 6
____________________
3 1 6 2
3 6 8 9
____________________________
4 0 0 5 5
12.
7 8 5
x
6 6
____________________
4 7 1 0
4 7 1 0
____________________________
5 1 8 1 1
13.
8 4 4
x
5 9
____________________
7 5 9 6
4 2 2 0
____________________________
4 9 7 9 9
14.
5 0 4
x
6 5
____________________
2 5 2 0
3 0 2 4
____________________________
3 2 7 6 6
15.
7 0 6
x
8 2
____________________
1 4 1 2
5 6 4 8
____________________________
5 7 8 9 9
16.
4 3 4
x
5 9
____________________
3 9 0 6
2 1 7 0
____________________________
2 5 6 0 0
17.
6 9 7
x
6 3
____________________
2 0 9 1
4 1 8 2
____________________________
4 3 9 1 1
18.
4 6 3
x
8 9
____________________
4 1 6 7
3 7 0 4
____________________________
4 1 2 0 0
19.
5 0 8
x
9 8
____________________
4 0 6 4
4 5 7 2
____________________________
4 9 7 8 8
20.
7 4 9
x
7 5
____________________
3 7 4 5
5 2 4 3
____________________________
5 6 1 7 7
21.
6 7 5
x
8 4
____________________
2 7 0 0
5 4 0 0
____________________________
5 6 7 0 0
22.
6 9 7
x
7 4
____________________
2 7 8 8
4 8 7 9
____________________________
5 1 5 7 7
23.
4 2 4
x
4 9
____________________
3 8 1 6
1 6 9 6
____________________________
2 0 7 7 7
24.
5 3 7
x
7 4
____________________
2 1 4 8
3 7 5 9
____________________________
3 9 7 3 3
25.
6 4 5
x
4 3
____________________
1 9 3 5
2 5 8 0
____________________________
2 7 7 3 3
26.
9 4 9
x
4 5
____________________
4 7 4 5
3 7 9 6
____________________________
4 2 7 0 0
27.
9 0 5
x
9 6
____________________
5 4 3 0
8 1 4 5
____________________________
8 6 8 8 8
28.
5 9 5
x
5 4
____________________
2 3 8 0
2 9 7 5
____________________________
3 2 1 3 3
29.
7 6 3
x
8 8
____________________
6 1 0 4
6 1 0 4
____________________________
6 7 1 4 4
30.
7 3 5
x
4 4
____________________
2 9 4 0
2 9 4 0
____________________________
3 2 3 4 4
31.
6 1 7
x
6 5
____________________
3 0 8 5
3 7 0 2
____________________________
4 0 1 0 0
32.
4 1 2
x
4 3
____________________
1 2 3 6
1 6 4 8
____________________________
1 7 7 1 1
33.
8 3 6
x
5 2
____________________
1 6 7 2
4 1 8 0
____________________________
4 3 4 7 7
34.
8 1 7
x
7 8
____________________
6 5 3 6
5 7 1 9
____________________________
6 3 7 2 2
35.
8 4 5
x
9 8
____________________
6 7 6 0
7 6 0 5
____________________________
8 2 8 1 1
36.
7 8 4
x
5 4
____________________
3 1 3 6
3 9 2 0
____________________________
4 2 3 3 3
37.
8 0 7
x
6 2
____________________
1 6 1 4
4 8 4 2
____________________________
5 0 0 3 3
38.
7 5 4
x
4 8
____________________
6 0 3 2
3 0 1 6
____________________________
3 6 1 9 9
39.
9 1 7
x
9 2
____________________
1 8 3 4
8 2 5 3
____________________________
8 4 3 6 6
40.
8 0 7
x
7 5
____________________
4 0 3 5
5 6 4 9
____________________________
6 0 5 2 2
41.
9 5 2
x
4 6
____________________
5 7 1 2
3 8 0 8
____________________________
4 3 7 9 9
42.
4 3 6
x
8 6
____________________
2 6 1 6
3 4 8 8
____________________________
3 7 4 9 9
43.
7 8 8
x
9 5
____________________
3 9 4 0
7 0 9 2
____________________________
7 4 8 6 6
44.
4 3 6
x
5 9
____________________
3 9 2 4
2 1 8 0
____________________________
2 5 7 2 2
45.
7 9 1
x
4 8
____________________
6 3 2 8
3 1 6 4
____________________________
3 7 9 6 6
46.
4 6 8
x
8 5
____________________
2 3 4 0
3 7 4 4
____________________________
3 9 7 8 8
47.
7 4 9
x
8 7
____________________
5 2 4 3
5 9 9 2
____________________________
6 5 1 6 6
48.
8 4 9
x
9 8
____________________
6 7 9 2
7 6 4 1
____________________________
8 3 2 0 0
49.
7 2 9
x
5 2
____________________
1 4 5 8
3 6 4 5
____________________________
3 7 9 0 0
50.
8 9 9
x
7 9
____________________
8 0 9 1
6 2 9 3
____________________________
7 1 0 2 2
51.
9 1 3
x
5 8
____________________
7 3 0 4
4 5 6 5
____________________________
5 2 9 5 5
52.
9 8 5
x
4 7
____________________
6 8 9 5
3 9 4 0
____________________________
4 6 2 9 9
53.
9 0 2
x
5 4
____________________
3 6 0 8
4 5 1 0
____________________________
4 8 7 0 0
54.
6 2 4
x
8 8
____________________
4 9 9 2
4 9 9 2
____________________________
5 4 9 1 1
55.
6 7 6
x
9 2
____________________
1 3 5 2
6 0 8 4
____________________________
6 2 1 9 9
56.
9 3 5
x
7 2
____________________
1 8 7 0
6 5 4 5
____________________________
6 7 3 2 2
57.
6 1 4
x
8 2
____________________
1 2 2 8
4 9 1 2
____________________________
5 0 3 4 4
58.
7 2 4
x
5 3
____________________
2 1 7 2
3 6 2 0
____________________________
3 8 3 7 7
59.
8 0 9
x
9 4
____________________
3 2 3 6
7 2 8 1
____________________________
7 6 0 4 4
60.
5 0 9
x
8 2
____________________
1 0 1 8
4 0 7 2
____________________________
4 1 7 3 3
61.
6 7 8
x
8 9
____________________
6 1 0 2
5 4 2 4
____________________________
6 0 3 4 4
62.
6 8 4
x
7 9
____________________
6 1 5 6
4 7 8 8
____________________________
5 4 0 3 3
63.
5 2 4
x
8 3
____________________
1 5 7 2
4 1 9 2
____________________________
4 3 4 9 9
64.
5 7 6
x
7 3
____________________
1 7 2 8
4 0 3 2
____________________________
4 2 0 4 4
65.
5 0 9
x
9 3
____________________
1 5 2 7
4 5 8 1
____________________________
4 7 3 3 3
66.
4 9 7
x
8 6
____________________
2 9 8 2
3 9 7 6
____________________________
4 2 7 4 4
67.
9 1 6
x
7 8
____________________
7 3 2 8
6 4 1 2
____________________________
7 1 4 4 4
68.
5 8 3
x
4 3
____________________
1 7 4 9
2 3 3 2
____________________________
2 5 0 6 6
69.
8 1 3
x
6 5
____________________
4 0 6 5
4 8 7 8
____________________________
5 2 8 4 4
70.
8 4 5
x
7 7
____________________
5 9 1 5
5 9 1 5
____________________________
6 5 0 6 6
71.
7 1 8
x
8 4
____________________
2 8 7 2
5 7 4 4
____________________________
6 0 3 1 1
72.
6 0 2
x
4 4
____________________
2 4 0 8
2 4 0 8
____________________________
2 6 4 8 8
73.
5 1 2
x
4 5
____________________
2 5 6 0
2 0 4 8
____________________________
2 3 0 4 4
74.
8 8 1
x
9 6
____________________
5 2 8 6
7 9 2 9
____________________________
8 4 5 7 7
75.
8 6 2
x
8 7
____________________
6 0 3 4
6 8 9 6
____________________________
7 4 9 9 9
76.
5 8 3
x
5 3
____________________
1 7 4 9
2 9 1 5
____________________________
3 0 8 9 9
77.
5 7 6
x
8 2
____________________
1 1 5 2
4 6 0 8
____________________________
4 7 2 3 3
78.
6 9 3
x
9 5
____________________
3 4 6 5
6 2 3 7
____________________________
6 5 8 3 3
79.
6 1 7
x
4 4
____________________
2 4 6 8
2 4 6 8
____________________________
2 7 1 4 4
80.
5 4 9
x
6 7
____________________
3 8 4 3
3 2 9 4
____________________________
3 6 7 8 8
81.
7 2 3
x
6 8
____________________
5 7 8 4
4 3 3 8
____________________________
4 9 1 6 6
82.
5 8 7
x
9 7
____________________
4 1 0 9
5 2 8 3
____________________________
5 6 9 3 3
83.
6 3 8
x
8 5
____________________
3 1 9 0
5 1 0 4
____________________________
5 4 2 3 3
84.
5 9 5
x
6 3
____________________
1 7 8 5
3 5 7 0
____________________________
3 7 4 8 8
85.
8 5 5
x
6 6
____________________
5 1 3 0
5 1 3 0
____________________________
5 6 4 3 3
86.
5 7 6
x
5 4
____________________
2 3 0 4
2 8 8 0
____________________________
3 1 1 0 0
87.
7 1 8
x
5 8
____________________
5 7 4 4
3 5 9 0
____________________________
4 1 6 4 4
88.
8 2 3
x
5 6
____________________
4 9 3 8
4 1 1 5
____________________________
4 6 0 8 8
89.
9 7 3
x
7 2
____________________
1 9 4 6
6 8 1 1
____________________________
7 0 0 5 5
90.
8 1 2
x
8 9
____________________
7 3 0 8
6 4 9 6
____________________________
7 2 2 6 6
91.
7 0 9
x
8 4
____________________
2 8 3 6
5 6 7 2
____________________________
5 9 5 5 5
92.
6 3 4
x
5 5
____________________
3 1 7 0
3 1 7 0
____________________________
3 4 8 7 7
93.
6 0 5
x
5 7
____________________
4 2 3 5
3 0 2 5
____________________________
3 4 4 8 8
94.
9 9 4
x
9 8
____________________
7 9 5 2
8 9 4 6
____________________________
9 7 4 1 1
95.
5 4 7
x
7 9
____________________
4 9 2 3
3 8 2 9
____________________________
4 3 2 1 1
96.
9 5 3
x
8 8
____________________
7 6 2 4
7 6 2 4
____________________________
8 3 8 6 6
97.
9 8 5
x
4 3
____________________
2 9 5 5
3 9 4 0
____________________________
4 2 3 5 5
98.
8 4 6
x
6 3
____________________
2 5 3 8
5 0 7 6
____________________________
5 3 2 9 9
99.
6 5 9
x
4 4
____________________
2 6 3 6
2 6 3 6
____________________________
2 8 9 9 9
100.
8 5 3
x
5 9
____________________
7 6 7 7
4 2 6 5
____________________________
5 0 3 2 2
101.
6 9 9
x
4 6
____________________
4 1 9 4
2 7 9 6
____________________________
3 2 1 5 5
102.
6 1 5
x
6 7
____________________
4 3 0 5
3 6 9 0
____________________________
4 1 2 0 0
103.
4 9 7
x
5 6
____________________
2 9 8 2
2 4 8 5
____________________________
2 7 8 3 3
104.
7 5 3
x
7 2
____________________
1 5 0 6
5 2 7 1
____________________________
5 4 2 1 1
105.
9 3 4
x
6 5
____________________
4 6 7 0
5 6 0 4
____________________________
6 0 7 1 1
106.
9 4 5
x
4 4
____________________
3 7 8 0
3 7 8 0
____________________________
4 1 5 8 8
107.
4 5 5
x
4 3
____________________
1 3 6 5
1 8 2 0
____________________________
1 9 5 6 6
108.
7 2 7
x
8 9
____________________
6 5 4 3
5 8 1 6
____________________________
6 4 7 0 0
109.
4 2 8
x
8 5
____________________
2 1 4 0
3 4 2 4
____________________________
3 6 3 8 8
110.
4 7 4
x
4 5
____________________
2 3 7 0
1 8 9 6
____________________________
2 1 3 3 3
111.
7 5 9
x
9 2
____________________
1 5 1 8
6 8 3 1
____________________________
6 9 8 2 2
112.
8 0 5
x
8 9
____________________
7 2 4 5
6 4 4 0
____________________________
7 1 6 4 4
113.
7 3 7
x
8 4
____________________
2 9 4 8
5 8 9 6
____________________________
6 1 9 0 0
114.
6 9 1
x
9 3
____________________
2 0 7 3
6 2 1 9
____________________________
6 4 2 6 6
115.
6 2 5
x
4 4
____________________
2 5 0 0
2 5 0 0
____________________________
2 7 5 0 0
116.
8 6 8
x
6 8
____________________
6 9 4 4
5 2 0 8
____________________________
5 9 0 2 2
117.
8 5 5
x
5 4
____________________
3 4 2 0
4 2 7 5
____________________________
4 6 1 7 7
118.
5 9 3
x
7 4
____________________
2 3 7 2
4 1 5 1
____________________________
4 3 8 8 8
119.
7 4 4
x
8 7
____________________
5 2 0 8
5 9 5 2
____________________________
6 4 7 2 2
120.
5 3 9
x
4 8
____________________
4 3 1 2
2 1 5 6
____________________________
2 5 8 7 7
121.
7 5 1
x
9 2
____________________
1 5 0 2
6 7 5 9
____________________________
6 9 0 9 9
122.
4 6 6
x
6 3
____________________
1 3 9 8
2 7 9 6
____________________________
2 9 3 5 5
123.
4 4 8
x
7 7
____________________
3 1 3 6
3 1 3 6
____________________________
3 4 4 9 9
124.
8 6 2
x
9 7
____________________
6 0 3 4
7 7 5 8
____________________________
8 3 6 1 1
125.
4 1 2
x
6 6
____________________
2 4 7 2
2 4 7 2
____________________________
2 7 1 9 9
126.
8 4 1
x
5 6
____________________
5 0 4 6
4 2 0 5
____________________________
4 7 0 9 9
127.
8 4 7
x
9 3
____________________
2 5 4 1
7 6 2 3
____________________________
7 8 7 7 7
128.
4 1 6
x
5 6
____________________
2 4 9 6
2 0 8 0
____________________________
2 3 2 9 9
129.
5 1 3
x
5 9
____________________
4 6 1 7
2 5 6 5
____________________________
3 0 2 6 6
130.
7 0 2
x
4 3
____________________
2 1 0 6
2 8 0 8
____________________________
3 0 1 8 8
131.
9 0 6
x
9 7
____________________
6 3 4 2
8 1 5 4
____________________________
8 7 8 8 8
132.
8 1 4
x
7 4
____________________
3 2 5 6
5 6 9 8
____________________________
6 0 2 3 3
133.
6 3 3
x
4 3
____________________
1 8 9 9
2 5 3 2
____________________________
2 7 2 1 1
134.
6 4 4
x
9 8
____________________
5 1 5 2
5 7 9 6
____________________________
6 3 1 1 1
135.
7 5 4
x
9 8
____________________
6 0 3 2
6 7 8 6
____________________________
7 3 8 9 9
136.
9 1 2
x
7 3
____________________
2 7 3 6
6 3 8 4
____________________________
6 6 5 7 7
137.
8 0 5
x
5 3
____________________
2 4 1 5
4 0 2 5
____________________________
4 2 6 6 6
138.
4 1 9
x
7 3
____________________
1 2 5 7
2 9 3 3
____________________________
3 0 5 8 8
139.
7 8 3
x
6 7
____________________
5 4 8 1
4 6 9 8
____________________________
5 2 4 6 6
140.
5 6 4
x
9 5
____________________
2 8 2 0
5 0 7 6
____________________________
5 3 5 8 8
141.
7 8 8
x
5 9
____________________
7 0 9 2
3 9 4 0
____________________________
4 6 4 9 9
142.
8 1 3
x
8 8
____________________
6 5 0 4
6 5 0 4
____________________________
7 1 5 4 4
143.
6 1 4
x
9 9
____________________
5 5 2 6
5 5 2 6
____________________________
6 0 7 8 8
144.
7 6 3
x
7 8
____________________
6 1 0 4
5 3 4 1
____________________________
5 9 5 1 1
145.
4 0 2
x
9 7
____________________
2 8 1 4
3 6 1 8
____________________________
3 8 9 9 9
146.
8 1 8
x
4 8
____________________
6 5 4 4
3 2 7 2
____________________________
3 9 2 6 6
147.
6 5 7
x
7 5
____________________
3 2 8 5
4 5 9 9
____________________________
4 9 2 7 7
148.
8 1 7
x
7 2
____________________
1 6 3 4
5 7 1 9
____________________________
5 8 8 2 2
149.
8 1 9
x
6 6
____________________
4 9 1 4
4 9 1 4
____________________________
5 4 0 5 5
150.
4 6 8
x
6 7
____________________
3 2 7 6
2 8 0 8
____________________________
3 1 3 5 5