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The key lies in a characteristic of the number 9. If you transpose the digits in a number and subtract the smaller number from the larger, the difference is always evenly divisible by 9.

Example 1

4321 rearranged to 1423

4321 minus 1423 = 2898

I choose to circle the 9, leaving the numbers 2, 8 & 8 to be typed in.

The only number that may be added to the sequence 2+8+8 and be divisible evenly by 9 is 9 (the digit I circled). [2+8+8+9=27]

Example 2

6734 rearranged to 7346

7346 minus 6734 = 612

I choose to circle the 6, leaving the numbers 1 & 2 to be typed in.

The only number that may be added to the sequence 1+2 and be divisible evenly by 9 is 6 (the digit I circled). [1+2+6=9]

Example 3

578 rearranged to 857

857 minus 578 = 279

I choose to circle the 2, leaving the numbers 7 & 9 to be typed in.

The only number that may be added to the sequence 7+9 and be divisible evenly by 9 is 2 (the digit I circled). [7+9+2=18]

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14y ago

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