1,234
1,243
1,324
........
........
+4,321
The addition problem above shows four of the 24 different integers that can be formed by using each of the digits 1, 2, 3, and 4 exactly once in each integer. What is the sum of these 24 integers?
24,000
26,664
40,440
60,000
66,660
粗心,每个数应该出现 6次不是4次
告诉了一共是24个数,说明以任何一个数作为千位的数会有6个。
一共24个数,每个数在每个位数出现6次,每个位数相加=1*6+2*6+3*6+4*6=60
再考虑分别处于个位、10位、百位、千位,和=60+600+6000+60000=66660
https://gmatclub.com/forum/the-addition-problem-above-shows-four-of-the-24-different-integers-tha-104166.html
这24个数中千位、百位、十位、个位的和都是60
60*(10^3 + 10^2 + 10 + 1) = 66660