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public class Question459 {
¡¡public static void main(String[] args) {
¡¡¡¡int sum = 0;
¡¡¡¡for (int i = 1; i <= 99; ++i) sum += ((139*i)/100)*100;
¡¡¡¡System.out.println(sum);
¡¡}
}
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139 * n = 100 * a + b ¤È¤«¤±¤ë¤È¤¹¤ë¤È¡¢
139 * (100 - n) = 139 * 100 - (100 * a + b) = (138 - a) * 100 + (100 - b) ¤È¤Ê¤ê¡¢
(139 * n ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = b¡¡<----->¡¡(139 * (100 - n) ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = 100 - b
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(139 * n ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * (100 - n) ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = 100
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(139 * 1 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 99 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = 39 + 61 = 100
(139 * 2 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 98 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = 78 + 22 = 100
¡¥¡¥¡¥
(139 * 49 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 51 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = 11 + 89 = 100
(139 * 50 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 50 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) = 50 + 50 = 100
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¤µ¤Æ¡¢µá¤á¤ëÁíϤϡ¢139 * 1, 139 * 2, ..., 139 * 99 ¤ÎÁíϤ«¤é¡¢ÀÚ¤ê¼Î¤Æ¤¿ 100 ¤Ç³ä¤Ã¤¿Í¾¤ê¤ÎÁíϤò°ú¤±¤Ð¤¤¤¤¤Î¤Ç¡¢
139 * n ¤È 139 * (100 - n) ¤È¤ÎÁȹ礻¤Ç¡¢139 * n + 139 * (100 - n) = 139 * 100 ¤È¡¢n = 50 ¤Î¾ì¹ç¤Î­¤·¤¹¤®¤ò¹Íθ¤·¤Æ¡¢
(µá¤á¤ëÁíÏÂ) = 139 * 100 * 50 - 100 * 50 - (139 * 50 - 50) = 138 * 100 * 50 - 138 * 50 = 138 * 99 * 50 = 683100
[·×»»ÊýË¡¤ò¤Á¤ç¤Ã¤ÈÄɲÃ]
(µá¤á¤ëÁíÏÂ)
= {139 * 1 + 139 * 2 + ... + 139 * 99}
- {(139 * 1 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 2 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + ... + (139 * 98 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 99 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê)}
¤Ç¤¹¤¬¡¢ÁÇľ¤Ë¡¢
2 * (µá¤á¤ëÁíÏÂ)
= {(139 * 1 + 139 * 99) + (139 * 2 + 139 * 98) + ... + (139 * 98 + 139 * 2) + (139 * 99 + 139 * 1)}
- {((139 * 1 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 99 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê)) + ((139 * 2 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 98 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê))
+ ...
+ ((139 * 98 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 2 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê)) + ((139 * 99 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê) + (139 * 1 ¤ò 100 ¤Ç³ä¤Ã¤¿Í¾¤ê))}
= 139 * 100 * 99 - 100 * 99
= 138 * 100 * 99
¤è¤ê¡¢
(µá¤á¤ëÁíÏÂ) = 138 * 100 * 99 / 2 = 683100
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139 * n = 100 * a + b ¤È¤«¤±¤ë¤È¤¹¤ë¤È¡¢
139 * (100 - n) = 139 * 100 - (100 * a + b) = (138 - a) * 100 + (100 - b) ¤È¤Ê¤ê¡¢
(139 * n ¤ò 100 ¤Ç³ä¤Ã¤¿¾¦) + (139 * (100 - n) ¤ò 100 ¤Ç³ä¤Ã¤¿¾¦) = a + (138 - a) = 138
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2 * (µá¤á¤ëÁíÏÂ) = (138 * 100) * 99
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(µá¤á¤ëÁíÏÂ) = (138 * 100) * 99 / 2 = 683100
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/*
* Created on 2005/07/19
*
* To change the template for this generated file go to
* Window&gt;Preferences&gt;Java&gt;Code Generation&gt;Code and Comments
*/
package mainPrograms;

public class Problem139 {
static final int MOTO = 139;
static int answer = 0;

public static void main(String[] args) {
for(int i = 1;i <= 99;i++){
System.out.println(i);
int y = MOTO * i;
int z;
String yS = Integer.toString(y);
String s = yS.substring(0,yS.length()-2);

System.out.println("139¤«¤±¤¿¿ô»ú¡§" + yS);
int kirisute = Integer.parseInt(s) * 100;
System.out.println("100¤Î°Ì°Ê²¼¤òÀÚ¤ê¼Î¤Æ¤¿¿ô»ú¡§" + kirisute);
answer += kirisute;
System.out.println("º£¤Þ¤Ç¤Î¹ç·×" + answer);
}
System.out.println("Á´Éô¤Î¹ç·×:" + answer);
}
}
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