Each letter represents a number. What are they?

The sum of AA+BB+CC+DD must be a multiple of 1 1, then A+C-B=0 or 1 1.

A, B and C are different, because the maximum number is 99+88+77+66=330, so A < =3.

So if A+C=B, there can be A= 1 B=3 C=2(A=2 C= 1, regardless), then DD =132-1-22-33.

A= 1 B=4 C=3, then DD =143-1-44-33 = 55 and D=5.

A= 1 B=5 C=4, then DD =154-1-55-44 = 44, D=4, the same as c, excluded.

A= 1 B=6 C=5, then DD =165-1-66-55 = 33 and D=3.

A= 1 B=7 C=6, then DD =176-1-77-66 = 22 and D=2.

A= 1 B=8 C=7, then DD =187-1-88-77 =11,D = 1, the same as a.

A= 1 B=9 C=8, then DD =198-1-99-88 = 0, excluding.

If A=2, then 2BC-22=BB+CC, and the maximum value of BB+CC is 187, that is, the maximum value of 2BC is 209, which is obviously impossible. Rule out! A=3 or more is even more impossible.

If A+C= 1 1+B, because a can only be 1, even +9 can only get 10, obviously this situation does not exist!

To sum up, if ABCD is different, then * * * has the following four solutions.

1 1+33+22+66= 132

1 1+44+33+55= 143

1 1+66+55+33= 165

1 1+77+66+22= 176

2.A*A+B*B+C*C+D*D=ABC

Each letter represents a number. What are they?

1* 1+ 1* 1+9*9+6*6= 1 19

1* 1+3*3+8*8+8*8= 138

1* 1+4*4+7*7+9*9= 147

1* 1+6*6+7*7+9*9= 167

1* 1+7*7+8*8+8*8= 178

1* 1+9*9+9*9+6*6= 199

3. Fill in the blanks with 1 ~ 9 to make it an equation:

□□□□□÷□□+□-□=2007

862 15÷43+9-7=2007

4. One of the most difficult puzzles:

/+? +? -? =2008

Use ten numbers at a time.

458 16/23+7+9-0=2008

45908/23+6+7- 1=2008

5 1948/26+3+7-0=2008

76 190/38+2+5-4=2008

86 172/43+0+9-5=2008

5. There is a kind of "out-of-shape calculation" in the puzzle, which generally includes two levels of operation.

For example:

90÷2+ 13×6

=45+78

= 123

Except for the number 123, every number from 0 to 9 is used once.

□□÷□+□□×□

=□□+□□

=?

(60/4)+(29*3)= 15+87= 102

(60/4)+(39*2)= 15+78=93

(78/2)+( 15*4)=39+60=99

(78/6)+(45*2)= 13+90= 103

(87/3)+( 15*4)=29+60=89

(90/2)+( 13*6)=45+78= 123