What pattern do you see in the first 9 multiples of 9?

Answer 1

Yes. Have a look:

09

18

27

36

45

54

63

72

81

90

The left column is numbered 0 to 9 and the right column is numbered 9 to 0, but that's only to 90. After that the pattern changes.

Answer 2

In the multiples of nine, you take the sum of the digits in each number, and you have 9, or another multiple of nine.

Examples:

9 * 6 = 54 ... 5 + 4 = 9

9 * 3 = 27 ... 2 + 7 = 9

9 * 140 = 1260 ... 1 + 2 + 6 + 0 + 9

9 * 487 = 4383 ... 4 + 3 + 8 + 3 = 18 ... 1 + 8 = 9

Answer 3

Yes, they all leave no remainder when divided by 7.

If you are looking for a pattern in the digits, there is one, but it is not simple.

• Partition the number into the units digit, U, and the preceding digits P.
  
• Calculate P - 2*U
• If the answer is divisible by +/-7 then the original number is a multiple of 7.
• If the answer is too large to test for divisibility by 7 easily then partition the answer and continue.

For example, consider

94675 => P = 9467, U = 5. P - 2*U = 9467 - 10 = 9457.

That may be too large so repeat.

9457 => P = 945, U = 7. P - 2*U = 945 - 14 = 931; still too large.

931 => P = 93, U = 1. P - 2*U = 93 - 2 = 91. 84 = 13*7 so 94668 is a multiple of 7. But you could continue.

91 => P = 9, U = 1. P - 2*U = 9 - 2 = 7 which is obviously a multiple of 7. So the original number is.

Note that the final "answer" can be a negative multiple of 7 or even 0.

Answer 4

The tens digits increase by one, while the ones digits decrease by one.

Answer 5

All digits will add up to 9 when one keeps adding until he/she gets a single digit.

Answer 6

If you sum all the digits in the number and, if the answer is greater than 9, repeat the process again and again, the final answer is 9.

Answer 7

Each multiple of 7 is 7 greater than the previous one.

Answer 8

The sum of all the digits is 9 or a multiple of 9.

Answer 9

It counts down 87654321

Answer 10

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