Gyakorlati alapok
Szorzáshegyek, azaz a tizes szorzólista
Adott egy probléma: szorzólistát kell írnunk. (A következő fejezetben az alábbiak alapján már könnyen fogunk írni szorzótáblát.) Mindehhez kell...
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szorzó * szorzandó = szorzat,
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és a számok, valamint a művelet ciklikus végrehajtása, mivel listaszerűen fogjuk ezeket kiszámolni és kiírni.
Természetesen a szorzólista más programozási módszerekkel is megoldható, de nagy valószínűséggel az egymásba ágyazott for ciklusok szolgáltatják az optimális megoldást (Ágyazzunk be a for ciklusnak! /az egybeágyazott for ciklusok/ című fejezet alapján). Nézzük a futtatható Java-kódot:
public class Main {
public static void main(String[] args) {
for (int i = 1; i <= 10; i++){
for (int j =
1; j <= 10; j++){
System.out.println(i + " * " + j + " = " + (i * j));
}
}
}
}
Végeredmény:
1 * 1 = 1
1 * 2 = 2
1 * 3 = 3
1 * 4 = 4
1 * 5 = 5
1 * 6 = 6
1 * 7 = 7
1 * 8 = 8
1 * 9 = 9
1 * 10 = 10
2 * 1 = 2
2 * 2 = 4
2 * 3 = 6
2 * 4 = 8
2 * 5 = 10
2 * 6 = 12
2 * 7 = 14
2 * 8 = 16
2 * 9 = 18
2 * 10 = 20
3 * 1 = 3
3 * 2 = 6
3 * 3 = 9
3 * 4 = 12
3 * 5 = 15
3 * 6 = 18
3 * 7 = 21
3 * 8 = 24
3 * 9 = 27
3 * 10 = 30
4 * 1 = 4
4 * 2 = 8
4 * 3 = 12
4 * 4 = 16
4 * 5 = 20
4 * 6 = 24
4 * 7 = 28
4 * 8 = 32
4 * 9 = 36
4 * 10 = 40
5 * 1 = 5
5 * 2 = 10
5 * 3 = 15
5 * 4 = 20
5 * 5 = 25
5 * 6 = 30
5 * 7 = 35
5 * 8 = 40
5 * 9 = 45
5 * 10 = 50
6 * 1 = 6
6 * 2 = 12
6 * 3 = 18
6 * 4 = 24
6 * 5 = 30
6 * 6 = 36
6 * 7 = 42
6 * 8 = 48
6 * 9 = 54
6 * 10 = 60
7 * 1 = 7
7 * 2 = 14
7 * 3 = 21
7 * 4 = 28
7 * 5 = 35
7 * 6 = 42
7 * 7 = 49
7 * 8 = 56
7 * 9 = 63
7 * 10 = 70
8 * 1 = 8
8 * 2 = 16
8 * 3 = 24
8 * 4 = 32
8 * 5 = 40
8 * 6 = 48
8 * 7 = 56
8 * 8 = 64
8 * 9 = 72
8 * 10 = 80
9 * 1 = 9
9 * 2 = 18
9 * 3 = 27
9 * 4 = 36
9 * 5 = 45
9 * 6 = 54
9 * 7 = 63
9 * 8 = 72
9 * 9 = 81
9 * 10 = 90
10 * 1 = 10
10 * 2 = 20
10 * 3 = 30
10 * 4 = 40
10 * 5 = 50
10 * 6 = 60
10 * 7 = 70
10 * 8 = 80
10 * 9 = 90
10 * 10 = 100
2 db for ciklusunk van. A külső ciklus i léptetője a szorzó, míg a belső j változó a szorzandó. Mivel 0-val való szorzásnak nincs értelme, a ciklusok 1-től indulnak és 10-ig tartanak (int i = 1; i <= 10; i++). Az egymásba ágyazott ciklusok működését fontos megértenünk, ezt a szorzótáblán kiválóan tudjuk tanulmányozni, ám akik számára még mindig nem átlátható, az alábbi kódban a következő módosítást tesszük:
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i-hez k betűt illesztünk (külső ciklusérték),
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j-hez b betűt illesztünk (belső ciklusérték.
Fontos észrevennünk, hogy ha k értéke nem változik (például 1k, 1k, 1k, stb.), akkor ott nincs (külső) ciklusfutás!
public class Main {
public static void main(String[] args) {
for (int i = 1; i <= 10; i++){
for (int j =
1; j <= 10; j++){
System.out.println(i + "k" + " * " + j + "b" + " = " + (i * j));
}
}
}
}
Végeredmény:
1k * 1b = 1
1k * 2b = 2
1k * 3b = 3
1k * 4b = 4
1k * 5b = 5
1k * 6b = 6
1k * 7b = 7
1k * 8b = 8
1k * 9b = 9
1k * 10b = 10
2k * 1b = 2
2k * 2b = 4
2k * 3b = 6
2k * 4b = 8
2k * 5b = 10
2k * 6b = 12
2k * 7b = 14
2k * 8b = 16
2k * 9b = 18
2k * 10b = 20
3k * 1b = 3
3k * 2b = 6
3k * 3b = 9
3k * 4b = 12
3k * 5b = 15
3k * 6b = 18
3k * 7b = 21
3k * 8b = 24
3k * 9b = 27
3k * 10b = 30
4k * 1b = 4
4k * 2b = 8
4k * 3b = 12
4k * 4b = 16
4k * 5b = 20
4k * 6b = 24
4k * 7b = 28
4k * 8b = 32
4k * 9b = 36
4k * 10b = 40
5k * 1b = 5
5k * 2b = 10
5k * 3b = 15
5k * 4b = 20
5k * 5b = 25
5k * 6b = 30
5k * 7b = 35
5k * 8b = 40
5k * 9b = 45
5k * 10b = 50
6k * 1b = 6
6k * 2b = 12
6k * 3b = 18
6k * 4b = 24
6k * 5b = 30
6k * 6b = 36
6k * 7b = 42
6k * 8b = 48
6k * 9b = 54
6k * 10b = 60
7k * 1b = 7
7k * 2b = 14
7k * 3b = 21
7k * 4b = 28
7k * 5b = 35
7k * 6b = 42
7k * 7b = 49
7k * 8b = 56
7k * 9b = 63
7k * 10b = 70
8k * 1b = 8
8k * 2b = 16
8k * 3b = 24
8k * 4b = 32
8k * 5b = 40
8k * 6b = 48
8k * 7b = 56
8k * 8b = 64
8k * 9b = 72
8k * 10b = 80
9k * 1b = 9
9k * 2b = 18
9k * 3b = 27
9k * 4b = 36
9k * 5b = 45
9k * 6b = 54
9k * 7b = 63
9k * 8b = 72
9k * 9b = 81
9k * 10b = 90
10k * 1b = 10
10k * 2b = 20
10k * 3b = 30
10k * 4b = 40
10k * 5b = 50
10k * 6b = 60
10k * 7b = 70
10k * 8b = 80
10k * 9b = 90
10k * 10b = 100
A kódból és a végeredményből kiolvasható, hogy 1 db külső ciklus lefutása után 10 db belső ciklusfutás következik. Ám a kiírás valójában megtévesztő, hiszen a 10 db 1k kiírás ellenére...
1k * 1b = 1
1k * 2b = 2
1k * 3b = 3
1k * 4b = 4
1k * 5b = 5
1k * 6b = 6
1k * 7b = 7
1k * 8b = 8
1k * 9b = 9
1k * 10b = 10
...a külső ciklus csakis 1x fut le (viszont a belső ciklusban valóban 10x van kiírva az i értéke).
Fontos észrevennünk, hogy ez a 2 dolog különböző!
Ezt úgy tudjuk leellenőrizni, hogy a belső ciklusból kihagyjuk i kiírását, a külsőbe helyezzük és csak a műveletet hagyjuk benne (i * j * k):
public class Main {
public static void main(String[] args) {
for (int i = 1; i <= 10; i++){
System.out.println(i + "k");
for (int j =
1; j <= 10; j++){
System.out.println(" * " + j + "b" + " = " + (i * j));
}
}
}
}
Végeredmény:
1k
* 1b = 1
* 2b = 2
* 3b = 3
* 4b = 4
* 5b = 5
* 6b = 6
* 7b = 7
* 8b = 8
* 9b = 9
* 10b = 10
2k
* 1b = 2
* 2b = 4
* 3b = 6
* 4b = 8
* 5b = 10
* 6b = 12
* 7b = 14
* 8b = 16
* 9b = 18
* 10b = 20
3k
* 1b = 3
* 2b = 6
stb...
Mindezek után azt hiszem viszonylag könnyű úgy módosítanunk a kódot, hogy 3 szám szorzását végezze el. Ehhez 1 további belső ciklust kell hozzáadnunk int k változóval:
public class Main {
public static void main(String[] args) {
for (int i = 1; i <= 10; i++){
for (int j =
1; j <= 10; j++){
for (int k = 1; k <= 10; k++){
System.out.println(i + " * " + j + " * " + k + " = " + (i * j * k));
}
}
}
}
}
Végeredmény:
1 * 1 * 1 = 1
1 * 1 * 2 = 2
1 * 1 * 3 = 3
1 * 1 * 4 = 4
1 * 1 * 5 = 5
1 * 1 * 6 = 6
1 * 1 * 7 = 7
1 * 1 * 8 = 8
1 * 1 * 9 = 9
1 * 1 * 10 = 10
1 * 2 * 1 = 2
1 * 2 * 2 = 4
1 * 2 * 3 = 6
1 * 2 * 4 = 8
1 * 2 * 5 = 10
1 * 2 * 6 = 12
1 * 2 * 7 = 14
1 * 2 * 8 = 16
1 * 2 * 9 = 18
1 * 2 * 10 = 20
1 * 3 * 1 = 3
1 * 3 * 2 = 6
1 * 3 * 3 = 9
1 * 3 * 4 = 12
1 * 3 * 5 = 15
1 * 3 * 6 = 18
1 * 3 * 7 = 21
1 * 3 * 8 = 24
1 * 3 * 9 = 27
1 * 3 * 10 = 30
1 * 4 * 1 = 4
1 * 4 * 2 = 8
1 * 4 * 3 = 12
1 * 4 * 4 = 16
1 * 4 * 5 = 20
1 * 4 * 6 = 24
1 * 4 * 7 = 28
1 * 4 * 8 = 32
1 * 4 * 9 = 36
1 * 4 * 10 = 40
1 * 5 * 1 = 5
1 * 5 * 2 = 10
1 * 5 * 3 = 15
1 * 5 * 4 = 20
1 * 5 * 5 = 25
1 * 5 * 6 = 30
1 * 5 * 7 = 35
1 * 5 * 8 = 40
1 * 5 * 9 = 45
1 * 5 * 10 = 50
1 * 6 * 1 = 6
1 * 6 * 2 = 12
1 * 6 * 3 = 18
1 * 6 * 4 = 24
1 * 6 * 5 = 30
1 * 6 * 6 = 36
1 * 6 * 7 = 42
1 * 6 * 8 = 48
1 * 6 * 9 = 54
1 * 6 * 10 = 60
1 * 7 * 1 = 7
1 * 7 * 2 = 14
1 * 7 * 3 = 21
1 * 7 * 4 = 28
1 * 7 * 5 = 35
1 * 7 * 6 = 42
1 * 7 * 7 = 49
1 * 7 * 8 = 56
1 * 7 * 9 = 63
1 * 7 * 10 = 70
1 * 8 * 1 = 8
1 * 8 * 2 = 16
1 * 8 * 3 = 24
1 * 8 * 4 = 32
1 * 8 * 5 = 40
1 * 8 * 6 = 48
1 * 8 * 7 = 56
1 * 8 * 8 = 64
1 * 8 * 9 = 72
1 * 8 * 10 = 80
1 * 9 * 1 = 9
1 * 9 * 2 = 18
1 * 9 * 3 = 27
1 * 9 * 4 = 36
1 * 9 * 5 = 45
1 * 9 * 6 = 54
1 * 9 * 7 = 63
1 * 9 * 8 = 72
1 * 9 * 9 = 81
1 * 9 * 10 = 90
1 * 10 * 1 = 10
1 * 10 * 2 = 20
1 * 10 * 3 = 30
1 * 10 * 4 = 40
1 * 10 * 5 = 50
1 * 10 * 6 = 60
1 * 10 * 7 = 70
1 * 10 * 8 = 80
1 * 10 * 9 = 90
1 * 10 * 10 = 100
2 * 1 * 1 = 2
2 * 1 * 2 = 4
2 * 1 * 3 = 6
2 * 1 * 4 = 8
2 * 1 * 5 = 10
2 * 1 * 6 = 12
2 * 1 * 7 = 14
2 * 1 * 8 = 16
2 * 1 * 9 = 18
2 * 1 * 10 = 20
2 * 2 * 1 = 4
2 * 2 * 2 = 8
2 * 2 * 3 = 12
2 * 2 * 4 = 16
2 * 2 * 5 = 20
2 * 2 * 6 = 24
2 * 2 * 7 = 28
2 * 2 * 8 = 32
2 * 2 * 9 = 36
2 * 2 * 10 = 40
2 * 3 * 1 = 6
2 * 3 * 2 = 12
2 * 3 * 3 = 18
2 * 3 * 4 = 24
2 * 3 * 5 = 30
2 * 3 * 6 = 36
2 * 3 * 7 = 42
2 * 3 * 8 = 48
2 * 3 * 9 = 54
2 * 3 * 10 = 60
2 * 4 * 1 = 8
2 * 4 * 2 = 16
2 * 4 * 3 = 24
2 * 4 * 4 = 32
2 * 4 * 5 = 40
2 * 4 * 6 = 48
2 * 4 * 7 = 56
2 * 4 * 8 = 64
2 * 4 * 9 = 72
2 * 4 * 10 = 80
2 * 5 * 1 = 10
2 * 5 * 2 = 20
2 * 5 * 3 = 30
2 * 5 * 4 = 40
2 * 5 * 5 = 50
2 * 5 * 6 = 60
2 * 5 * 7 = 70
2 * 5 * 8 = 80
2 * 5 * 9 = 90
2 * 5 * 10 = 100
2 * 6 * 1 = 12
2 * 6 * 2 = 24
2 * 6 * 3 = 36
2 * 6 * 4 = 48
2 * 6 * 5 = 60
2 * 6 * 6 = 72
2 * 6 * 7 = 84
2 * 6 * 8 = 96
2 * 6 * 9 = 108
2 * 6 * 10 = 120
2 * 7 * 1 = 14
2 * 7 * 2 = 28
2 * 7 * 3 = 42
2 * 7 * 4 = 56
2 * 7 * 5 = 70
2 * 7 * 6 = 84
2 * 7 * 7 = 98
2 * 7 * 8 = 112
2 * 7 * 9 = 126
2 * 7 * 10 = 140
2 * 8 * 1 = 16
2 * 8 * 2 = 32
2 * 8 * 3 = 48
2 * 8 * 4 = 64
2 * 8 * 5 = 80
2 * 8 * 6 = 96
2 * 8 * 7 = 112
2 * 8 * 8 = 128
2 * 8 * 9 = 144
2 * 8 * 10 = 160
2 * 9 * 1 = 18
2 * 9 * 2 = 36
2 * 9 * 3 = 54
2 * 9 * 4 = 72
2 * 9 * 5 = 90
2 * 9 * 6 = 108
2 * 9 * 7 = 126
2 * 9 * 8 = 144
2 * 9 * 9 = 162
2 * 9 * 10 = 180
2 * 10 * 1 = 20
2 * 10 * 2 = 40
2 * 10 * 3 = 60
2 * 10 * 4 = 80
2 * 10 * 5 = 100
2 * 10 * 6 = 120
2 * 10 * 7 = 140
2 * 10 * 8 = 160
2 * 10 * 9 = 180
2 * 10 * 10 = 200
3 * 1 * 1 = 3
3 * 1 * 2 = 6
3 * 1 * 3 = 9
3 * 1 * 4 = 12
3 * 1 * 5 = 15
3 * 1 * 6 = 18
3 * 1 * 7 = 21
3 * 1 * 8 = 24
3 * 1 * 9 = 27
3 * 1 * 10 = 30
3 * 2 * 1 = 6
3 * 2 * 2 = 12
3 * 2 * 3 = 18
3 * 2 * 4 = 24
3 * 2 * 5 = 30
3 * 2 * 6 = 36
3 * 2 * 7 = 42
3 * 2 * 8 = 48
3 * 2 * 9 = 54
3 * 2 * 10 = 60
3 * 3 * 1 = 9
3 * 3 * 2 = 18
3 * 3 * 3 = 27
3 * 3 * 4 = 36
3 * 3 * 5 = 45
3 * 3 * 6 = 54
3 * 3 * 7 = 63
3 * 3 * 8 = 72
3 * 3 * 9 = 81
3 * 3 * 10 = 90
3 * 4 * 1 = 12
3 * 4 * 2 = 24
3 * 4 * 3 = 36
3 * 4 * 4 = 48
3 * 4 * 5 = 60
3 * 4 * 6 = 72
3 * 4 * 7 = 84
3 * 4 * 8 = 96
3 * 4 * 9 = 108
3 * 4 * 10 = 120
3 * 5 * 1 = 15
3 * 5 * 2 = 30
3 * 5 * 3 = 45
3 * 5 * 4 = 60
3 * 5 * 5 = 75
3 * 5 * 6 = 90
3 * 5 * 7 = 105
3 * 5 * 8 = 120
3 * 5 * 9 = 135
3 * 5 * 10 = 150
3 * 6 * 1 = 18
3 * 6 * 2 = 36
3 * 6 * 3 = 54
3 * 6 * 4 = 72
3 * 6 * 5 = 90
3 * 6 * 6 = 108
3 * 6 * 7 = 126
3 * 6 * 8 = 144
3 * 6 * 9 = 162
3 * 6 * 10 = 180
3 * 7 * 1 = 21
3 * 7 * 2 = 42
3 * 7 * 3 = 63
3 * 7 * 4 = 84
3 * 7 * 5 = 105
3 * 7 * 6 = 126
3 * 7 * 7 = 147
3 * 7 * 8 = 168
3 * 7 * 9 = 189
3 * 7 * 10 = 210
3 * 8 * 1 = 24
3 * 8 * 2 = 48
3 * 8 * 3 = 72
3 * 8 * 4 = 96
3 * 8 * 5 = 120
3 * 8 * 6 = 144
3 * 8 * 7 = 168
3 * 8 * 8 = 192
3 * 8 * 9 = 216
3 * 8 * 10 = 240
3 * 9 * 1 = 27
3 * 9 * 2 = 54
3 * 9 * 3 = 81
3 * 9 * 4 = 108
3 * 9 * 5 = 135
3 * 9 * 6 = 162
3 * 9 * 7 = 189
3 * 9 * 8 = 216
3 * 9 * 9 = 243
3 * 9 * 10 = 270
3 * 10 * 1 = 30
3 * 10 * 2 = 60
3 * 10 * 3 = 90
3 * 10 * 4 = 120
3 * 10 * 5 = 150
3 * 10 * 6 = 180
3 * 10 * 7 = 210
3 * 10 * 8 = 240
3 * 10 * 9 = 270
3 * 10 * 10 = 300
4 * 1 * 1 = 4
4 * 1 * 2 = 8
4 * 1 * 3 = 12
4 * 1 * 4 = 16
4 * 1 * 5 = 20
4 * 1 * 6 = 24
4 * 1 * 7 = 28
4 * 1 * 8 = 32
4 * 1 * 9 = 36
4 * 1 * 10 = 40
4 * 2 * 1 = 8
4 * 2 * 2 = 16
4 * 2 * 3 = 24
4 * 2 * 4 = 32
4 * 2 * 5 = 40
4 * 2 * 6 = 48
4 * 2 * 7 = 56
4 * 2 * 8 = 64
4 * 2 * 9 = 72
4 * 2 * 10 = 80
4 * 3 * 1 = 12
4 * 3 * 2 = 24
4 * 3 * 3 = 36
4 * 3 * 4 = 48
4 * 3 * 5 = 60
4 * 3 * 6 = 72
4 * 3 * 7 = 84
4 * 3 * 8 = 96
4 * 3 * 9 = 108
4 * 3 * 10 = 120
4 * 4 * 1 = 16
4 * 4 * 2 = 32
4 * 4 * 3 = 48
4 * 4 * 4 = 64
4 * 4 * 5 = 80
4 * 4 * 6 = 96
4 * 4 * 7 = 112
4 * 4 * 8 = 128
4 * 4 * 9 = 144
4 * 4 * 10 = 160
4 * 5 * 1 = 20
4 * 5 * 2 = 40
4 * 5 * 3 = 60
4 * 5 * 4 = 80
4 * 5 * 5 = 100
4 * 5 * 6 = 120
4 * 5 * 7 = 140
4 * 5 * 8 = 160
4 * 5 * 9 = 180
4 * 5 * 10 = 200
4 * 6 * 1 = 24
4 * 6 * 2 = 48
4 * 6 * 3 = 72
4 * 6 * 4 = 96
4 * 6 * 5 = 120
4 * 6 * 6 = 144
4 * 6 * 7 = 168
4 * 6 * 8 = 192
4 * 6 * 9 = 216
4 * 6 * 10 = 240
4 * 7 * 1 = 28
4 * 7 * 2 = 56
4 * 7 * 3 = 84
4 * 7 * 4 = 112
4 * 7 * 5 = 140
4 * 7 * 6 = 168
4 * 7 * 7 = 196
4 * 7 * 8 = 224
4 * 7 * 9 = 252
4 * 7 * 10 = 280
4 * 8 * 1 = 32
4 * 8 * 2 = 64
4 * 8 * 3 = 96
4 * 8 * 4 = 128
4 * 8 * 5 = 160
4 * 8 * 6 = 192
4 * 8 * 7 = 224
4 * 8 * 8 = 256
4 * 8 * 9 = 288
4 * 8 * 10 = 320
4 * 9 * 1 = 36
4 * 9 * 2 = 72
4 * 9 * 3 = 108
4 * 9 * 4 = 144
4 * 9 * 5 = 180
4 * 9 * 6 = 216
4 * 9 * 7 = 252
4 * 9 * 8 = 288
4 * 9 * 9 = 324
4 * 9 * 10 = 360
4 * 10 * 1 = 40
4 * 10 * 2 = 80
4 * 10 * 3 = 120
4 * 10 * 4 = 160
4 * 10 * 5 = 200
4 * 10 * 6 = 240
4 * 10 * 7 = 280
4 * 10 * 8 = 320
4 * 10 * 9 = 360
4 * 10 * 10 = 400
5 * 1 * 1 = 5
5 * 1 * 2 = 10
5 * 1 * 3 = 15
5 * 1 * 4 = 20
5 * 1 * 5 = 25
5 * 1 * 6 = 30
5 * 1 * 7 = 35
5 * 1 * 8 = 40
5 * 1 * 9 = 45
5 * 1 * 10 = 50
5 * 2 * 1 = 10
5 * 2 * 2 = 20
5 * 2 * 3 = 30
5 * 2 * 4 = 40
5 * 2 * 5 = 50
5 * 2 * 6 = 60
5 * 2 * 7 = 70
5 * 2 * 8 = 80
5 * 2 * 9 = 90
5 * 2 * 10 = 100
5 * 3 * 1 = 15
5 * 3 * 2 = 30
5 * 3 * 3 = 45
5 * 3 * 4 = 60
5 * 3 * 5 = 75
5 * 3 * 6 = 90
5 * 3 * 7 = 105
5 * 3 * 8 = 120
5 * 3 * 9 = 135
5 * 3 * 10 = 150
5 * 4 * 1 = 20
5 * 4 * 2 = 40
5 * 4 * 3 = 60
5 * 4 * 4 = 80
5 * 4 * 5 = 100
5 * 4 * 6 = 120
5 * 4 * 7 = 140
5 * 4 * 8 = 160
5 * 4 * 9 = 180
5 * 4 * 10 = 200
5 * 5 * 1 = 25
5 * 5 * 2 = 50
5 * 5 * 3 = 75
5 * 5 * 4 = 100
5 * 5 * 5 = 125
5 * 5 * 6 = 150
5 * 5 * 7 = 175
5 * 5 * 8 = 200
5 * 5 * 9 = 225
5 * 5 * 10 = 250
5 * 6 * 1 = 30
5 * 6 * 2 = 60
5 * 6 * 3 = 90
5 * 6 * 4 = 120
5 * 6 * 5 = 150
5 * 6 * 6 = 180
5 * 6 * 7 = 210
5 * 6 * 8 = 240
5 * 6 * 9 = 270
5 * 6 * 10 = 300
5 * 7 * 1 = 35
5 * 7 * 2 = 70
5 * 7 * 3 = 105
5 * 7 * 4 = 140
5 * 7 * 5 = 175
5 * 7 * 6 = 210
5 * 7 * 7 = 245
5 * 7 * 8 = 280
5 * 7 * 9 = 315
5 * 7 * 10 = 350
5 * 8 * 1 = 40
5 * 8 * 2 = 80
5 * 8 * 3 = 120
5 * 8 * 4 = 160
5 * 8 * 5 = 200
5 * 8 * 6 = 240
5 * 8 * 7 = 280
5 * 8 * 8 = 320
5 * 8 * 9 = 360
5 * 8 * 10 = 400
5 * 9 * 1 = 45
5 * 9 * 2 = 90
5 * 9 * 3 = 135
5 * 9 * 4 = 180
5 * 9 * 5 = 225
5 * 9 * 6 = 270
5 * 9 * 7 = 315
5 * 9 * 8 = 360
5 * 9 * 9 = 405
5 * 9 * 10 = 450
5 * 10 * 1 = 50
5 * 10 * 2 = 100
5 * 10 * 3 = 150
5 * 10 * 4 = 200
5 * 10 * 5 = 250
5 * 10 * 6 = 300
5 * 10 * 7 = 350
5 * 10 * 8 = 400
5 * 10 * 9 = 450
5 * 10 * 10 = 500
6 * 1 * 1 = 6
6 * 1 * 2 = 12
6 * 1 * 3 = 18
6 * 1 * 4 = 24
6 * 1 * 5 = 30
6 * 1 * 6 = 36
6 * 1 * 7 = 42
6 * 1 * 8 = 48
6 * 1 * 9 = 54
6 * 1 * 10 = 60
6 * 2 * 1 = 12
6 * 2 * 2 = 24
6 * 2 * 3 = 36
6 * 2 * 4 = 48
6 * 2 * 5 = 60
6 * 2 * 6 = 72
6 * 2 * 7 = 84
6 * 2 * 8 = 96
6 * 2 * 9 = 108
6 * 2 * 10 = 120
6 * 3 * 1 = 18
6 * 3 * 2 = 36
6 * 3 * 3 = 54
6 * 3 * 4 = 72
6 * 3 * 5 = 90
6 * 3 * 6 = 108
6 * 3 * 7 = 126
6 * 3 * 8 = 144
6 * 3 * 9 = 162
6 * 3 * 10 = 180
6 * 4 * 1 = 24
6 * 4 * 2 = 48
6 * 4 * 3 = 72
6 * 4 * 4 = 96
6 * 4 * 5 = 120
6 * 4 * 6 = 144
6 * 4 * 7 = 168
6 * 4 * 8 = 192
6 * 4 * 9 = 216
6 * 4 * 10 = 240
6 * 5 * 1 = 30
6 * 5 * 2 = 60
6 * 5 * 3 = 90
6 * 5 * 4 = 120
6 * 5 * 5 = 150
6 * 5 * 6 = 180
6 * 5 * 7 = 210
6 * 5 * 8 = 240
6 * 5 * 9 = 270
6 * 5 * 10 = 300
6 * 6 * 1 = 36
6 * 6 * 2 = 72
6 * 6 * 3 = 108
6 * 6 * 4 = 144
6 * 6 * 5 = 180
6 * 6 * 6 = 216
6 * 6 * 7 = 252
6 * 6 * 8 = 288
6 * 6 * 9 = 324
6 * 6 * 10 = 360
6 * 7 * 1 = 42
6 * 7 * 2 = 84
6 * 7 * 3 = 126
6 * 7 * 4 = 168
6 * 7 * 5 = 210
6 * 7 * 6 = 252
6 * 7 * 7 = 294
6 * 7 * 8 = 336
6 * 7 * 9 = 378
6 * 7 * 10 = 420
6 * 8 * 1 = 48
6 * 8 * 2 = 96
6 * 8 * 3 = 144
6 * 8 * 4 = 192
6 * 8 * 5 = 240
6 * 8 * 6 = 288
6 * 8 * 7 = 336
6 * 8 * 8 = 384
6 * 8 * 9 = 432
6 * 8 * 10 = 480
6 * 9 * 1 = 54
6 * 9 * 2 = 108
6 * 9 * 3 = 162
6 * 9 * 4 = 216
6 * 9 * 5 = 270
6 * 9 * 6 = 324
6 * 9 * 7 = 378
6 * 9 * 8 = 432
6 * 9 * 9 = 486
6 * 9 * 10 = 540
6 * 10 * 1 = 60
6 * 10 * 2 = 120
6 * 10 * 3 = 180
6 * 10 * 4 = 240
6 * 10 * 5 = 300
6 * 10 * 6 = 360
6 * 10 * 7 = 420
6 * 10 * 8 = 480
6 * 10 * 9 = 540
6 * 10 * 10 = 600
7 * 1 * 1 = 7
7 * 1 * 2 = 14
7 * 1 * 3 = 21
7 * 1 * 4 = 28
7 * 1 * 5 = 35
7 * 1 * 6 = 42
7 * 1 * 7 = 49
7 * 1 * 8 = 56
7 * 1 * 9 = 63
7 * 1 * 10 = 70
7 * 2 * 1 = 14
7 * 2 * 2 = 28
7 * 2 * 3 = 42
7 * 2 * 4 = 56
7 * 2 * 5 = 70
7 * 2 * 6 = 84
7 * 2 * 7 = 98
7 * 2 * 8 = 112
7 * 2 * 9 = 126
7 * 2 * 10 = 140
7 * 3 * 1 = 21
7 * 3 * 2 = 42
7 * 3 * 3 = 63
7 * 3 * 4 = 84
7 * 3 * 5 = 105
7 * 3 * 6 = 126
7 * 3 * 7 = 147
7 * 3 * 8 = 168
7 * 3 * 9 = 189
7 * 3 * 10 = 210
7 * 4 * 1 = 28
7 * 4 * 2 = 56
7 * 4 * 3 = 84
7 * 4 * 4 = 112
7 * 4 * 5 = 140
7 * 4 * 6 = 168
7 * 4 * 7 = 196
7 * 4 * 8 = 224
7 * 4 * 9 = 252
7 * 4 * 10 = 280
7 * 5 * 1 = 35
7 * 5 * 2 = 70
7 * 5 * 3 = 105
7 * 5 * 4 = 140
7 * 5 * 5 = 175
7 * 5 * 6 = 210
7 * 5 * 7 = 245
7 * 5 * 8 = 280
7 * 5 * 9 = 315
7 * 5 * 10 = 350
7 * 6 * 1 = 42
7 * 6 * 2 = 84
7 * 6 * 3 = 126
7 * 6 * 4 = 168
7 * 6 * 5 = 210
7 * 6 * 6 = 252
7 * 6 * 7 = 294
7 * 6 * 8 = 336
7 * 6 * 9 = 378
7 * 6 * 10 = 420
7 * 7 * 1 = 49
7 * 7 * 2 = 98
7 * 7 * 3 = 147
7 * 7 * 4 = 196
7 * 7 * 5 = 245
7 * 7 * 6 = 294
7 * 7 * 7 = 343
7 * 7 * 8 = 392
7 * 7 * 9 = 441
7 * 7 * 10 = 490
7 * 8 * 1 = 56
7 * 8 * 2 = 112
7 * 8 * 3 = 168
7 * 8 * 4 = 224
7 * 8 * 5 = 280
7 * 8 * 6 = 336
7 * 8 * 7 = 392
7 * 8 * 8 = 448
7 * 8 * 9 = 504
7 * 8 * 10 = 560
7 * 9 * 1 = 63
7 * 9 * 2 = 126
7 * 9 * 3 = 189
7 * 9 * 4 = 252
7 * 9 * 5 = 315
7 * 9 * 6 = 378
7 * 9 * 7 = 441
7 * 9 * 8 = 504
7 * 9 * 9 = 567
7 * 9 * 10 = 630
7 * 10 * 1 = 70
7 * 10 * 2 = 140
7 * 10 * 3 = 210
7 * 10 * 4 = 280
7 * 10 * 5 = 350
7 * 10 * 6 = 420
7 * 10 * 7 = 490
7 * 10 * 8 = 560
7 * 10 * 9 = 630
7 * 10 * 10 = 700
8 * 1 * 1 = 8
8 * 1 * 2 = 16
8 * 1 * 3 = 24
8 * 1 * 4 = 32
8 * 1 * 5 = 40
8 * 1 * 6 = 48
8 * 1 * 7 = 56
8 * 1 * 8 = 64
8 * 1 * 9 = 72
8 * 1 * 10 = 80
8 * 2 * 1 = 16
8 * 2 * 2 = 32
8 * 2 * 3 = 48
8 * 2 * 4 = 64
8 * 2 * 5 = 80
8 * 2 * 6 = 96
8 * 2 * 7 = 112
8 * 2 * 8 = 128
8 * 2 * 9 = 144
8 * 2 * 10 = 160
8 * 3 * 1 = 24
8 * 3 * 2 = 48
8 * 3 * 3 = 72
8 * 3 * 4 = 96
8 * 3 * 5 = 120
8 * 3 * 6 = 144
8 * 3 * 7 = 168
8 * 3 * 8 = 192
8 * 3 * 9 = 216
8 * 3 * 10 = 240
8 * 4 * 1 = 32
8 * 4 * 2 = 64
8 * 4 * 3 = 96
8 * 4 * 4 = 128
8 * 4 * 5 = 160
8 * 4 * 6 = 192
8 * 4 * 7 = 224
8 * 4 * 8 = 256
8 * 4 * 9 = 288
8 * 4 * 10 = 320
8 * 5 * 1 = 40
8 * 5 * 2 = 80
8 * 5 * 3 = 120
8 * 5 * 4 = 160
8 * 5 * 5 = 200
8 * 5 * 6 = 240
8 * 5 * 7 = 280
8 * 5 * 8 = 320
8 * 5 * 9 = 360
8 * 5 * 10 = 400
8 * 6 * 1 = 48
8 * 6 * 2 = 96
8 * 6 * 3 = 144
8 * 6 * 4 = 192
8 * 6 * 5 = 240
8 * 6 * 6 = 288
8 * 6 * 7 = 336
8 * 6 * 8 = 384
8 * 6 * 9 = 432
8 * 6 * 10 = 480
8 * 7 * 1 = 56
8 * 7 * 2 = 112
8 * 7 * 3 = 168
8 * 7 * 4 = 224
8 * 7 * 5 = 280
8 * 7 * 6 = 336
8 * 7 * 7 = 392
8 * 7 * 8 = 448
8 * 7 * 9 = 504
8 * 7 * 10 = 560
8 * 8 * 1 = 64
8 * 8 * 2 = 128
8 * 8 * 3 = 192
8 * 8 * 4 = 256
8 * 8 * 5 = 320
8 * 8 * 6 = 384
8 * 8 * 7 = 448
8 * 8 * 8 = 512
8 * 8 * 9 = 576
8 * 8 * 10 = 640
8 * 9 * 1 = 72
8 * 9 * 2 = 144
8 * 9 * 3 = 216
8 * 9 * 4 = 288
8 * 9 * 5 = 360
8 * 9 * 6 = 432
8 * 9 * 7 = 504
8 * 9 * 8 = 576
8 * 9 * 9 = 648
8 * 9 * 10 = 720
8 * 10 * 1 = 80
8 * 10 * 2 = 160
8 * 10 * 3 = 240
8 * 10 * 4 = 320
8 * 10 * 5 = 400
8 * 10 * 6 = 480
8 * 10 * 7 = 560
8 * 10 * 8 = 640
8 * 10 * 9 = 720
8 * 10 * 10 = 800
9 * 1 * 1 = 9
9 * 1 * 2 = 18
9 * 1 * 3 = 27
9 * 1 * 4 = 36
9 * 1 * 5 = 45
9 * 1 * 6 = 54
9 * 1 * 7 = 63
9 * 1 * 8 = 72
9 * 1 * 9 = 81
9 * 1 * 10 = 90
9 * 2 * 1 = 18
9 * 2 * 2 = 36
9 * 2 * 3 = 54
9 * 2 * 4 = 72
9 * 2 * 5 = 90
9 * 2 * 6 = 108
9 * 2 * 7 = 126
9 * 2 * 8 = 144
9 * 2 * 9 = 162
9 * 2 * 10 = 180
9 * 3 * 1 = 27
9 * 3 * 2 = 54
9 * 3 * 3 = 81
9 * 3 * 4 = 108
9 * 3 * 5 = 135
9 * 3 * 6 = 162
9 * 3 * 7 = 189
9 * 3 * 8 = 216
9 * 3 * 9 = 243
9 * 3 * 10 = 270
9 * 4 * 1 = 36
9 * 4 * 2 = 72
9 * 4 * 3 = 108
9 * 4 * 4 = 144
9 * 4 * 5 = 180
9 * 4 * 6 = 216
9 * 4 * 7 = 252
9 * 4 * 8 = 288
9 * 4 * 9 = 324
9 * 4 * 10 = 360
9 * 5 * 1 = 45
9 * 5 * 2 = 90
9 * 5 * 3 = 135
9 * 5 * 4 = 180
9 * 5 * 5 = 225
9 * 5 * 6 = 270
9 * 5 * 7 = 315
9 * 5 * 8 = 360
9 * 5 * 9 = 405
9 * 5 * 10 = 450
9 * 6 * 1 = 54
9 * 6 * 2 = 108
9 * 6 * 3 = 162
9 * 6 * 4 = 216
9 * 6 * 5 = 270
9 * 6 * 6 = 324
9 * 6 * 7 = 378
9 * 6 * 8 = 432
9 * 6 * 9 = 486
9 * 6 * 10 = 540
9 * 7 * 1 = 63
9 * 7 * 2 = 126
9 * 7 * 3 = 189
9 * 7 * 4 = 252
9 * 7 * 5 = 315
9 * 7 * 6 = 378
9 * 7 * 7 = 441
9 * 7 * 8 = 504
9 * 7 * 9 = 567
9 * 7 * 10 = 630
9 * 8 * 1 = 72
9 * 8 * 2 = 144
9 * 8 * 3 = 216
9 * 8 * 4 = 288
9 * 8 * 5 = 360
9 * 8 * 6 = 432
9 * 8 * 7 = 504
9 * 8 * 8 = 576
9 * 8 * 9 = 648
9 * 8 * 10 = 720
9 * 9 * 1 = 81
9 * 9 * 2 = 162
9 * 9 * 3 = 243
9 * 9 * 4 = 324
9 * 9 * 5 = 405
9 * 9 * 6 = 486
9 * 9 * 7 = 567
9 * 9 * 8 = 648
9 * 9 * 9 = 729
9 * 9 * 10 = 810
9 * 10 * 1 = 90
9 * 10 * 2 = 180
9 * 10 * 3 = 270
9 * 10 * 4 = 360
9 * 10 * 5 = 450
9 * 10 * 6 = 540
9 * 10 * 7 = 630
9 * 10 * 8 = 720
9 * 10 * 9 = 810
9 * 10 * 10 = 900
10 * 1 * 1 = 10
10 * 1 * 2 = 20
10 * 1 * 3 = 30
10 * 1 * 4 = 40
10 * 1 * 5 = 50
10 * 1 * 6 = 60
10 * 1 * 7 = 70
10 * 1 * 8 = 80
10 * 1 * 9 = 90
10 * 1 * 10 = 100
10 * 2 * 1 = 20
10 * 2 * 2 = 40
10 * 2 * 3 = 60
10 * 2 * 4 = 80
10 * 2 * 5 = 100
10 * 2 * 6 = 120
10 * 2 * 7 = 140
10 * 2 * 8 = 160
10 * 2 * 9 = 180
10 * 2 * 10 = 200
10 * 3 * 1 = 30
10 * 3 * 2 = 60
10 * 3 * 3 = 90
10 * 3 * 4 = 120
10 * 3 * 5 = 150
10 * 3 * 6 = 180
10 * 3 * 7 = 210
10 * 3 * 8 = 240
10 * 3 * 9 = 270
10 * 3 * 10 = 300
10 * 4 * 1 = 40
10 * 4 * 2 = 80
10 * 4 * 3 = 120
10 * 4 * 4 = 160
10 * 4 * 5 = 200
10 * 4 * 6 = 240
10 * 4 * 7 = 280
10 * 4 * 8 = 320
10 * 4 * 9 = 360
10 * 4 * 10 = 400
10 * 5 * 1 = 50
10 * 5 * 2 = 100
10 * 5 * 3 = 150
10 * 5 * 4 = 200
10 * 5 * 5 = 250
10 * 5 * 6 = 300
10 * 5 * 7 = 350
10 * 5 * 8 = 400
10 * 5 * 9 = 450
10 * 5 * 10 = 500
10 * 6 * 1 = 60
10 * 6 * 2 = 120
10 * 6 * 3 = 180
10 * 6 * 4 = 240
10 * 6 * 5 = 300
10 * 6 * 6 = 360
10 * 6 * 7 = 420
10 * 6 * 8 = 480
10 * 6 * 9 = 540
10 * 6 * 10 = 600
10 * 7 * 1 = 70
10 * 7 * 2 = 140
10 * 7 * 3 = 210
10 * 7 * 4 = 280
10 * 7 * 5 = 350
10 * 7 * 6 = 420
10 * 7 * 7 = 490
10 * 7 * 8 = 560
10 * 7 * 9 = 630
10 * 7 * 10 = 700
10 * 8 * 1 = 80
10 * 8 * 2 = 160
10 * 8 * 3 = 240
10 * 8 * 4 = 320
10 * 8 * 5 = 400
10 * 8 * 6 = 480
10 * 8 * 7 = 560
10 * 8 * 8 = 640
10 * 8 * 9 = 720
10 * 8 * 10 = 800
10 * 9 * 1 = 90
10 * 9 * 2 = 180
10 * 9 * 3 = 270
10 * 9 * 4 = 360
10 * 9 * 5 = 450
10 * 9 * 6 = 540
10 * 9 * 7 = 630
10 * 9 * 8 = 720
10 * 9 * 9 = 810
10 * 9 * 10 = 900
10 * 10 * 1 = 100
10 * 10 * 2 = 200
10 * 10 * 3 = 300
10 * 10 * 4 = 400
10 * 10 * 5 = 500
10 * 10 * 6 = 600
10 * 10 * 7 = 700
10 * 10 * 8 = 800
10 * 10 * 9 = 900
10 * 10 * 10 = 1000
Pénzes László