Solve ABCDEF by 3 BCDEFA and calculate how many numbers each of them represents

Step 1 First, consider that the 6-digit number multiplied by 3 results in a 6-digit number, then its highest digit A can be up to 3 with three values.

Step 2 first substitute 1 into the single digit of the result, that is, a=1, only when the multiplier f=7, the unit digit a of the result is 1, and the f value is 7, and then substitute 7 into the f position of the result, and then continue to push backwards, only when the multiplier e=5, the result f is 7, and 5 is substituted into the position of the result e, backward the d value, only when the multiplier d=8, the result of e is 5, the 8 is substituted into the position of the result d, only when the multiplier c=2, the result of d is 8, and the position of substituting 2 into the result c, only the multiplier b=4, the result of c is 2, and all the results come out, abcdef=142857

Step 3 Substitute 2 into the unit of the result, and push it backwards according to the above steps--substitute--backwards, and get the result abcdef=285714

Step 4 Substitute 3 into the single digit of the result, and still push backwards according to the above steps - substitute - backwards, and the result is not valid.

In the end, there are two results. i.e. abcdef = 142857 or abcdef = 285714

Let bcdef=x, a=y3(100000y+x)=10x+y300000y+3x=10x+y7x=299999yx=42857y, when y=1, x=42857, when y=2, x=85714, so there are two sets of solutions: 142587 3=425871285714 3=857142

Let bcdef=x

a*100000+x]*m=10x+a

Because a six-digit multiplication by a single digit is still a six-digit number, it means that m is less than or equal to 3, and a is less than or equal to 3 when m=3 and a=3

3*100000+x]*3=10x+3

x=128571

When m=3, a=2

x=85714, suitable.

When m=3, a=1

x=42857, suitable.

When m=2, a=3

x=No. When m=2, a=2

x=No. It has been tested that when m=3, a=2 or 1 is appropriate.

That is: 285714*3=857142

Or: 142857*3=428571

Step 1 First, consider that the 6-digit number multiplied by 3 results in a 6-digit number, then its highest digit A can be up to 3 with three values.

Step 2 first substitute 1 into the single digit of the result, that is, a=1, only when the multiplier f=7, the unit digit a of the result is 1, and the f value is 7, and then substitute 7 into the f position of the result, and then continue to push backwards, only when the multiplier e=5, the result f is 7, and 5 is substituted into the position of the result e, backward the d value, only when the multiplier d=8, the result of e is 5, the 8 is substituted into the position of the result d, only when the multiplier c=2, the result of d is 8, and the position of substituting 2 into the result c, only the multiplier b=4, the result of c is 2, and all the results come out, abcdef=142857

Step 3 Substitute 2 into the unit of the result, and push backwards according to the above steps - substitute to get the result abcdef=285714

Step 4 Substitute 3 into the single digit of the result, and still substitute it backwards according to the above steps, and the result is not valid.

In the end, there are two results. i.e. abcdef = 142857 or abcdef = 285714

Set BCDEF to x3 (100000 A x) 10x A300000A 3x 10x A300000A A 7x299999a 7xx 42857AA, 1x 42857, 2x 85714, 285714 3=857142142857 3=428571

When the empirical calculation is in line with the meaning of the question, the value of a is greater than 2, and the x is 6 digits, which does not meet the meaning of the topic. So there are only two answers.

5 digits multiplied by 3 equals 5 digits, so a 3. A = 1, b = 4, c = 2, d = 8, e = 5, f = 7 and 2 are fruitless.

Let x=bcdef, then 3*(100000*a+x)=10*x+a, x=42857a, so the value of a is 1 or 2, x=bcdef=42857 or 85714, so bcdefa=428571 or 857142

Result: 142857 3=428571.

abcdef=142857

abcdef=100000a+s

3（100000a+s）=10s+a

7s=299999a

s=42857a, in addition, a can only be , if a is greater than or equal to 4, this number multiplied by 3 will become a 7-digit number.

a=1, the result is 142857 3=428571.

a=2, the result is 285714 3=571428, which does not fit the topic.

a=3, the result is 428571 3=1285713, which does not fit the topic.

Multiplication. It can also be thought of as calculating objects arranged in a rectangle (integer) or finding the area of a rectangle whose side length is given. The area of the rectangle does not depend on which side is measured first, which illustrates the swap property.

The result of the two measurements is a new type of measurement, for example, multiplying the lengths of both sides of a rectangle to give its area, which is the subject of dimensional analysis.

6 digits multiplied by 3 or 6 digits, a can only be 1 or 2 or 3, when a is 1, then f is 7 (only 7 and 3 times have a single digit 1) and to carry 2, then e can only be 5, only 5 and 3 times ten is 5, plus the 2 that comes up becomes 7, and so on, abcdef is 142857 respectively; When a is 2, abcdef is 285714 with the method just now; When A chooses 3, there is no answer.