perplexus.info :: Numbers : Six Digits = Triangle + Triangle

Six Digits = Triangle + Triangle (Posted on 2008-08-17)

There are three 6 digit numbers with the following properties applicable to each:

1. All digits are unique.
2. The first three digits ABC form a triangular number as do the latter three, DEF; both are multiples of 3.
3. The digital root/sum of the first triangular number is greater than that of the second.
4. Three consecutive digits form the difference of the triangular numbers, either being ascending or descending.

Identify the three 6 digit numbers.

Submitted by brianjn

Rating: 3.0000 (1 votes)

Solution: (Hide)

There are twenty-one triangular numbers having 3 digits, and are divisible by 3, of which 17 have unique digits. They are, listed according to their digital root/sum:

9 6 3 153 105 120 351 231 210 378 276 435 465 561 528 630 780 741 861 903
There are 6 pairings whereby the digital sum of the first 3 digits is greater than the second 3, and have consecutive digits as the difference, viz:
1st 2nd Diff 105 561 456 351 561 210 780 903 123 120 465 345 276 153 123 780 435 345
The first three have at least one digit that has been repeated.

The three numbers in question are, 120465, 276153 and 780435.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Analytical Solution	K Sengupta	2008-08-18 12:21:21
Solution	Dej Mar	2008-08-18 01:50:07
computer solution (spoiler)	Charlie	2008-08-17 18:58:46

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