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这是第36届美国中学数学竞赛的一题: 整数a由1985个数字8组成,整数b由1985个数字5组成,则整数9ab的各位数字的和是: (A)15880;(B)17856; (C)17865,(D)17874;(E)19851。原题的数目太大,退一步看看,a=8,b=5时易得9ab=360,各位数字的和是9=1×9;a=88,b=55时9ab=9·88·55=9·8·5·11~2=9·8·5·(10~2-1/9))~2=40·1/9·9801=43560。其各位数字之和是18=2×9。由此猜想原题的答案是1985·9=17865,
This is the subject of the 36th American High School Mathematics Contest: The integer a consists of 1985 digits 8, the integer b consists of 1985 digits 5, and the sum of the digits of the integer 9 ab is: (A) 15880; (B) 17856 ;(C)17865,(D)17874;(E)19851. The number of original questions is too large, take a step back and see, a = 8, b = 5 is easy to get 9ab = 360, the sum of the digits is 9 = 1 × 9; a = 88, b = 55 when 9ab = 9 · 88 55=9·8·5·11~2=9·8·5·(10~2-1/9))~2=40·1/9·9801=43560. The sum of its digits is 18=2×9. From this, the answer to the original question is 1985-9=17865.