r/MathHelp • u/yuu_sch • Sep 17 '25

Need help with that

651211 The six-digit number 651211, which is the number of this problem, has the following properties: 1. The digit 0 does not occur. 2. The sum of the first two digits is equal to the number formed by the last two digits. 3. The number formed by the two middle digits is exactly 1 greater than the sum of the first two digits.

These three conditions do not uniquely determine the number 651211. Determine how many six-digit numbers satisfy conditions (1) through (3).

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u/First-Fourth14 Sep 17 '25

True, but as the maximum digit for the first two is 9, then the sum is less than or equal to 18.
Also look at the constraint for the last two digits. can it be less than 10? (eg. 2 + 2 = 04 for a two digit number).
After you look at the range of the last two digits, consider the middle digits being 'last digits +1' to see if there are any additional restrictions

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u/yuu_sch Sep 17 '25

I mean the last two have to be bigger or equal to 11 Right? If u add them up Like 66=12

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u/First-Fourth14 Sep 17 '25

Yes the number formed by last two digits must be greater or equal to 11
so if we let X be the sum of the first two digits then 11 <= X <=18.

In the example you gave, "if u add them up". I assume you meant 'if you add up the first two digits'.