一個(gè)四位數(shù),若它的千位數(shù)字與個(gè)位數(shù)字相同,百位數(shù)字與十位數(shù)字相同,那么稱(chēng)這個(gè)四位數(shù)為“對(duì)稱(chēng)數(shù)”.
(1)最小的四位“對(duì)稱(chēng)數(shù)”是
1001
1001
,最大的四位“對(duì)稱(chēng)數(shù)”是
9999
9999
;
(2)若一個(gè)“對(duì)稱(chēng)數(shù)”的個(gè)位數(shù)字為a,十位數(shù)字為b,請(qǐng)用含a,b的代數(shù)式表示該“對(duì)稱(chēng)數(shù)”;
(3)判斷任意一個(gè)四位“對(duì)稱(chēng)數(shù)”能否被11整除,若能,請(qǐng)說(shuō)明理由,若不能,請(qǐng)舉出反例.