每周数学思维训练题

YIEYIE · 发表于 2003-12-15 15:30:51

1.(Hua 7) Observe that 12 = 1, 112 = 121, 1112 = 12321. For N = 11…12 (10 1’s), find the sum of the digits of N.

2.(CMC 9-98-23/11-98-21)Two numbers 123456789 and 999999999 are multiplied. How many of the digits in the final result are 9’s?

3.(CMC 10-99-12) The numbers 49, 29, 9, 40, 22, 15, 53, 33, 13, 47 are grouped in pairs so that the sum of each pair is the same. Which nu

chrisyue · 发表于 2004-3-16 11:16:51

1. 12=1
   1=1
112=121
      11
   11
   121
deduce 11111111112=1234567900987654321.
2.123456789*999999999=123456789*1000000000-123456789=1234567887654321.
so the digits of 9=0
3.49+29+9+40+22+15+53+33+13+47=310
310/5=62
62-49 =13
62-29=33
62-9=53
62-40=22