Math S4

2013-09-03 12:28 am
How many three-digit numbers satisfy the property that the middle digit is the
average of the first and the last digits?

回答 (2)

2013-09-03 1:25 am
✔ 最佳答案
生字:
satisfy 滿足
property  特性
average 平均數


所有結果:
111,123,135,147,159,
210,222,234,246,258,
321,333,345,357,369,
420,432,444,456,468,
531,543,555,567,579,
630,642,654,666,678,
741,753,765,777,789,
840,852,864,876,888,
951,963,975,987,999


當然,你唔洗好似我咁傻,列晒所有結果......
你只需列晒由"1"字開頭的便可→就可得知:每一個數字開頭都有5個 結果,
而3位數只可由1-9 (共有9個 )開頭.

所以ans.
=9*5
=45


2013-09-02 17:31:00 補充:
我一開頭低能到咁- -

111,222,333,444,555,666,777,888,999,
123,234,345,456,567,678,789,
135,246,357,468,579,
147,258,369,
210,420,630,840,
再倒轉2-4行......

真係笑大人個口,蠢到冇人有......

2013-09-02 17:34:04 補充:
唔係3位數只可由1-9開頭,
係每個位都只可由1-9開頭......

2013-09-02 17:35:47 補充:
又講錯- -'
係3位數嘅第一個位(百位)只可由1-9開頭......

2013-09-02 23:55:16 補充:
係喎~咁樣易諗d...
2013-09-03 7:50 am
也可以先諗中間果個亦見pattern:

?9? 有 999
?8? 有 987,888,789
?7? 有 975,876,777,678,579
?6? 有 963,864,765,666,567,468,369
?5? 有 951,...,159
?4? 有 147,246,345,444,543,642,741,840
?3? 有 135,234,333,432,531,630,
?2? 有 123,222,321,420
?1? 有 111,210

共:1+3+5+7+9+8+6+4+2=45


收錄日期: 2021-04-20 14:16:28
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