Contest Assistant
- Posts 55525
- WRZ$
677096.80
- Device Not Specified
You know us, here at Mobilism, always ready to help you learn new skills
In 2018, a paper was published demonstrating that every positive integer can be written as the sum of three palindromic numbers in every number system with base 5 or greater.
Let’s put that to the test
What is it?
- A contest where the goal is to find 3 palindromic numbers whose sum adds up to one of the numbers listed below.
- A palindromic number is a number that is the same when written forwards or backwards. The first few palindromic numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121…
- Any positive integer can be written as the sum of 3 palindromic numbers, at least once. For example: 81465 = 81418 + 44 + 3 or 81465 = 80408 + 969 + 88 or 81465 = 80708 + 555 + 202, etc.
- Here is a fairly easy way to break down any given number into the sum of 3 palindromic numbers
:- Find a large palindromic number close in value to the one you are trying to break down (for example, for 81465 you could use 81418; for 81409 you could try 81318).
- Subtract this palindromic number from your chosen number (for example, 81465-81418=47 or 81409-81318=91).
- Then find two palindromic numbers whose sum adds up to this remainder (47=44+3, 91=88+3).
- If it does not work or if you want to find another solution, try another large palindromic number within your target and so on (for example, 81465=81318+141+6, 81409=81218+191+0).
How do you play?
- Post one of the numbers listed below along with 3 palindromic numbers that will sum to get this number, but who are different from the example given in bracket.
- One post per number listed below at a time.
- You may make up to three separate posts.
Wade Van Landingham wrote:81465 = 80708 + 555 + 202
Rules:
- Each edition of Palindromic Trinity will be open for at least 48 hours.
- 3 posts maximum per person per round, any more and all of your posts will be disallowed.
- No duplicates.
- Where a post has been edited resulting in duplicates, then the last one in time gets disallowed.
Reward
- 20 WRZ$ for each valid post different from the given examples of breaking down.
- 0 WRZ$ for the posts identical to the given examples of breaking down.
2718583 (2010102 + 655556 + 52925)
2528665 (2011102 + 424424 + 93139)
9811396 (9101019 + 692296 + 18081)
1571898 (1101011 + 435534 + 35353)
3868855 (3111113 + 704407 + 53335)
1362182 (1011101 + 260062 + 91019)
7137409 (6110116 + 986689 + 40604)
6196477 (5200025 + 956659 + 39793)
2325768 (2001002 + 275572 + 49194)
3491374 (3100013 + 305503 + 85858)
1592532 (1111111 + 411114 + 70307)
7636312 (7200027 + 418814 + 17471)
164576 (76667 + 87778 + 131) and all the decompositions posted in that post http://forum.mobilism.org/viewtopic.php?p=7819688#7819688
4759084 (4110114 + 602206 + 46764)
4273037 (3300033 + 914419 + 58585)
2690916 (2001002 + 598895 + 91019)
2060292 (1100011 + 935539 + 24742)
8957946 (8201028 + 738837 + 18081)
6409459 (6111116 + 282282 + 16061)
3260612 (2300032 + 946649 + 13931)
8088169 (7110117 + 947749 + 30303)
Last edited by hija on Aug 26th, 2020, 6:45 pm, edited 2 times in total.
Reason: New rules
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