一筐鸡蛋:1个1个拿,正好拿完。2个2个拿,还剩1个。3个3个拿,正好拿完。4个4个拿,还剩1个。5个5个拿,还剩1个6个6个拿,还剩3个。7个7个拿,正好拿完。8个8个拿,还剩1个。9个9个拿,正好拿完。问筐里有多少鸡蛋?1个1个拿,正好拿完。3个3个拿,正好拿完。7个7个拿,正好拿完。9个9个拿,正好拿完。此数为7*9=63的倍数。设此数为63n2个2个拿,还剩1个。4个4个拿,还剩1个。5个5个拿,还剩1个,8个8个拿,还剩1个。此数为5*8=40的倍数+1个.设此数为40k+1即63n=40k+1k=(63n-1)/40因为n,k均为正整数所以当n=7时,K的最小值为11所以这筐鸡蛋的最小值为敬行63*7=40*11+1=441个。2个2个拿,还剩1个。4个4个拿,还剩1个。8个8个拿,还剩1个。说明篮子里的鸡蛋个数为奇数。3个3个拿,正好拿完。7个7个拿,正好拿完。9个9个拿,正好拿完。说明篮子里的鸡蛋个数为3、7与9的倍数。5个5个拿,还剩1个,说明个位数为1或6,最终个位数为1.。综合上面所说,最少的应该是441,这个数是2.4.5.8的倍数多1,是1.3.7.9的倍数,是6的倍数多3∴是441个3x7x3=6363对于4,5来说都余3,对于6余3,对于8余7,为了满足题意需要3x7x3=63在乘以一个不被2整除数3x7x3x7=63x7=4411个1个拿,正好拿完。......................441除1等于4412个2个拿,还剩1个。......................441除2等于220余13个3个拿,正好拿完。......................441除3等于1474个4个拿,还剩1个。.....................441除4等于110余15个5个拿,还剩1个.....................441除5等于88余16个6个拿,还剩3个。.....................441除6等于73余37个7个拿,正好拿完。.....................441除7等于638个8个拿,还剩1个亮颤哗洞冲。.....................441除8等于55余19个9个拿,正好拿完。.....................441除9等于49
标签:尝试,数学