标题: 牛人求救看看这道奇怪的数学题-OG 解释 不清晰 [打印本页] 作者: liuyongmei 时间: 2010-9-5 23:51 标题: 牛人求救看看这道奇怪的数学题-OG 解释 不清晰 11. Of the three-digit integers greater than 700, how many have two digits that are equal to each other and the remaining digit different from the other two? (A) 90 (B) 82 (C) 80 (D) 45 (E) 36
In three-digit integers, there are three pairs of digits that can be the same while the other digit is diff erent: tens and ones, hundreds and tens, and hundreds and ones. In each of these pairs, there are 9 options for having the third digit be diff erent from the other two. Th e single exception to this is in the 700–799 set, where the number 700 cannot be included because the problem calls for integers “greater than 700.” So, in the 700–799 set, there are only 8 options for when the tens and ones are the same. Th is is shown in the table below.
Number of digits available for the third digit when two given digits are the same Same 701–799 800–899 900–999 tens and ones 8 9 9 hundreds and tens 9 9 9 hundreds and ones 9 9 9
Th us, of the three-digit integers greater than 700, there are 9(9) – 1 = 80 numbers that have two digits that are equal to each other when the remaining digit is diff erent from these two. The correct answer is C.
我看不明白： 如果已经按照701–799这样的分法了，如何能得出tens and ones similar?毕竟这一组数里面百位数就是7。如果十位数，个位数再相同，那么就成了3位数字都一样了。