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Renhua Olympic Mathematical Problems
1,45|x 1993y? 5|x 1993y,9|x 1993y? y=0,5; 9|x+y+ 1+3=x+y+4

When y=0, x=5.

When y=5, x=9.

Yes, 5 19930 or 9 19935.

2, equivalent to horizontal crossword puzzle: 28×A.BC=9△.2△

Equivalent to 28×ABC=9△2△

So 4|9△2△? 4|2△? △=0,4,8

Divide 90.20, 94.24 and 98.28 by 28 respectively, and we can see that 98.28 can be exhausted, and the quotient is 3.5 1.

3, equivalent to 8|x93 1y, 9 | x931y.

8|x93 1y? 8|3 1y? y=2

9|x93 1y? 9|x+4+y? x=3

The qualified five-digit number is 393 12.

4, equivalent to 8| 154xy, 9| 154xy.

9| 154xy? 9|( 1+x+y)? X+y=8 or 17.

8| 154xy? 8|4xy

When x+y= 17, only xy=98 or 89, but neither of them can satisfy 8|4xy.

So x+y=8, (for example, 8|408)

5,2|32x5y? y=0,2,4,8

3|32x5y? 3|(2+x+5+y)? 3|(7+x+y)? x+y=2,5,8, 1 1, 14, 17

5|32x5y? y = 0,5

To sum up, y=0 and x=2, 5, 8.

Such five digits are 32250, 32550 and 32850.

6, easy to get 8|□67.9△? 8|79△? △=2

That is 9|□6792? 9|(□+6+7+9+2)? 9|(□+6)? □=3

So the unit price is 367.92÷72=5. 1 1 yuan.