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the question i'm assuming is asking for 4 digit numbers satisfying this property? the statements "first two sets of numbers" and "middle two sets of numbers" aren't precise otherwise.

so you're looking for numbers abcd.

10a+b+10c+d=10b+c, which can be rewritten 10a+d=9(b-c). Note that the LHS is just the two digit number ad, and it's a two digit multiple of 9 (because the RHS is 9(b-c)). so basically the 4 digit numbers in question are built by

1) taking a two digit multiple of 9, and using those two digits as the first and the last of the 4 digit number.

2) dividing the number in step 1) by 9 and picking two digits b and c (the middle ones) whose difference is the result.

e.g., take 54. then 5 and 4 will be the first and last digits. 54/9=6, so the middle digits should have a difference of 6. possibilities:

5604, 5714, 5824, 5934

<blockquote data-quote="pruse" data-source="post: 35286" data-attributes="member: 4633">the question i&#039;m assuming is asking for 4 digit numbers satisfying this property? the statements &quot;first two sets of numbers&quot; and &quot;middle two sets of numbers&quot; aren&#039;t precise otherwise.so you&#039;re looking for numbers abcd.10a+b+10c+d=10b+c, which can be rewritten 10a+d=9(b-c). Note that the LHS is just the two digit number ad, and it&#039;s a two digit multiple of 9 (because the RHS is 9(b-c)). so basically the 4 digit numbers in question are built by 1) taking a two digit multiple of 9, and using those two digits as the first and the last of the 4 digit number.2) dividing the number in step 1) by 9 and picking two digits b and c (the middle ones) whose difference is the result.e.g., take 54. then 5 and 4 will be the first and last digits. 54/9=6, so the middle digits should have a difference of 6. possibilities:5604, 5714, 5824, 5934</blockquote>

[QUOTE="pruse, post: 35286, member: 4633"] the question i'm assuming is asking for 4 digit numbers satisfying this property? the statements "first two sets of numbers" and "middle two sets of numbers" aren't precise otherwise. so you're looking for numbers abcd. 10a+b+10c+d=10b+c, which can be rewritten 10a+d=9(b-c). Note that the LHS is just the two digit number ad, and it's a two digit multiple of 9 (because the RHS is 9(b-c)). so basically the 4 digit numbers in question are built by 1) taking a two digit multiple of 9, and using those two digits as the first and the last of the 4 digit number. 2) dividing the number in step 1) by 9 and picking two digits b and c (the middle ones) whose difference is the result. e.g., take 54. then 5 and 4 will be the first and last digits. 54/9=6, so the middle digits should have a difference of 6. possibilities: 5604, 5714, 5824, 5934 [/QUOTE]

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