Abcdefghij joke

In the ten-digit abcdefghij, different letters represent different numbers. Where A is a multiple of 1, two ab is a multiple of 2, three abc is a multiple of 3, four abcd is a multiple of 4, five abcde is a multiple of 5, six abcdef is a multiple of 6, seven abcdefg is a multiple of 7, eight abcdefgh is a multiple of 8, nine abcdefghi is a multiple of 9 and ten abcdefghij is 6540. Find abcdefghij

Step 1: j is 0; (Decimal number abcdefghij is a multiple of 10)

Step 2: e is 5; (Five-digit abcde is a multiple of 5, but E cannot be 0)

Step 3: A, C, G and I are odd numbers, and B, D, F and H are even numbers; (The multiple mantissas of the remaining 2, 4, 6 and 8 are even)

Step 4: Try "Eight-bit abcdefgh is a multiple of 8". Fgh can be 216,296,416,432,472,496,632,672,816,832,872,896, and H can be.

Step 5: Try "six-digit abcdef is a multiple of 6", and the def can be 258,456,654,852;

Step 6: Combining the above steps 4 and 5, the defgh can be 25,865,438+06,25,896,45,632,45,672,65,432,85,265,438+06 and 85,296;

Step 7: Combining "four-digit abcd is a multiple of 4" with the results of step 3 and step 6, the defgh can be 258 16, 25896, 65432, 65472;

Step 8: Combining the results of step 7 with "two ab digits are multiples of 2 and three abc digits are multiples of 3", abcdefgh can be 14725896, 74 125896, 18965432, 78965432, 98/kl.

Step 9: Combining "seven-bit abcdefg is a multiple of 7" and the result of step 8, abcdefgh can be 38165472;

In other words, the whole decimal number is 38 16547290.