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The solution process of 20 1 1 Hunan college entrance examination mathematics 16.
16 solution: according to the meaning of the question, the natural number of 1- 127 can be discussed in different ranges with 2 n as the dividing point (note: n is 1, 2, 3, 4, 5, 6 respectively);

1, in 64- 127, can be expressed as: 2 6+2 5+2 4+2 3+2 2 1+2 0 (* * has 7 items), and the coefficient of each item is 65433. The numbers with 5-0 terms and a coefficient of 0 are C6 and 5 respectively; C6,4; C6,3; C6,2; C6, 1; C6,0 .

2. In 32-63, it can be expressed as: 2 5+24+23+22+2 1+20 (* *), and the coefficient of each item is1or 0, except "25". C5,4; C5,3; C5,2; C5, 1; C5,0 .

3. Similarly, in 16-3 1, the coefficients of 4-0 are C4 and 4 respectively; And 4; C4,3; C4,2; C4, 1; C4,0 .。

In 8- 15, the coefficient of 3-0 is 0: C3, 3; C3,2; C3, 1; C3,0 .。

In 4-7, the coefficient of 2-0 is 0: C2, 2; C2, 1; C2,0 .

In 2-3, the coefficient of 1-0 is 0: C 1,1; C 1,0 .

In 1, the term with a coefficient of 0 is 0.

In combination with the above,

The number of six numbers with coefficient 0 is C6, 6 =1;

The number of five numbers with a coefficient of 0 is C6, 5+C5, and 5 = 7;

The number of four numbers with coefficient 0 is C6, 4+C5, 4+C4, 4 = 21;

The number of three numbers with coefficient 0 is C6, 3+C5, 3+C4, 3+C3, 3 = 35;

The number of numbers with binomial coefficient of 0 is C6, 2+C5, 2+C4, 2+C3, 2+C2, 2 = 35;

The number of the term 1 with a coefficient of 0 is C6, 1+C5, 1+C4, 1+C3, 1+C2, 1+C 1,/kloc.

The number of numbers with a coefficient of 0 is C6, 0+C5, 0+C4, 0+C3, 0+C2, 0+C 1, 0+C0, 0 = 7.

The sum of the original problems is: 26x1+25x7+24x21+23x35+22x35+21x 21+20x7 = 64+224+336+24.