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Posted by **lori** on Sunday, November 4, 2012 at 1:49pm.

It states that John thinks of a 3-digit number. What is his number? Use the clues below to find John's number.

Every digit is different.

The sum of all thedigits is 19.

The difference between the hundreds digit and the ones digit is 6.

The tens digit is the greatest digit.

The number is greater than 500.

Please Help.

- singapore math -
**Ms. Sue**, Sunday, November 4, 2012 at 1:58pmUse trial and error.

The hundreds digit is 6, 7, 8, or 9

The ones digit is 0, 1, 2, or 3

The tens digit is 7, 8, or 9

Can you figure this out now?

- singapore math -
**Steve**, Sunday, November 4, 2012 at 1:58pmif hundreds-ones=6, then we have

9x3

8x2

7x1

6x0

Since the digits add to 19, 7x1 and 6x0 are out, leaving

9x3 or 8x2

If tens is greatest, 9x3 is out, so we must have

892

This must be the number, since the only other choice would be 298, where the difference between hundreds and ones is still 6, but in the other direction

- singapore math -
**Damon**, Sunday, November 4, 2012 at 2:24pmx y z

x + y + z = 19

|x-z| = 6

x >/= 5

y >/= 6

so x+y >/= 11

so z </= 8 to get 19 sum

z < 6 because y is biggest

choices

x 5 6 7 8 9

y 6 7 8 9

z 0 1 2 3 4 5 6 7 8

but x and z differ by 6 so

x 5 6 7 8 9

y 6 7 8 9

z 0 1 2 3

now what adds to 19 there with y biggest?

none until y = 9

so x 9 z

but x and z differ by six

8 and 2 differ by six

8 9 2 ?

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