Home > Oddly Triangular > Description

Oddly Triangular

AZsPCs | AP Math | Description

The Problem

Find the largest positive integer k that you can, subject to these constraints:

  1. k has only odd digits.
  2. The sum 1 + 2 + 3 + ... + k has only odd digits.

For example, both 17 and 1 + 2 + 3 + ... + 17 = 153 have only odd digits.

This problem is Shyam Sunder Gupta's CYF NO. 55 and is used with permission. Please note that on that web page there are several large numbers that satisfy the problem's constraints. These numbers are explicitly disqualified for submission to this contest.

The Contest

Submit your largest k on the Submit page. You may insert commas in the number to increase readability.

Over the course of the contest you may submit additional values for k, but only the largest integer you submit will count.

Each integer k receives a score equal to log10(k)+1. This is roughly equal to the number of digits of k.

For purposes of ranking solutions, in case of a tied score we give preference to the entry that was submitted first.

Getting Your Questions Answered

First, check the FAQ section below. If you can't find the information you need there, send your question to the discussion group. If your question is of a personal nature, and not of general interest, send an email directly to Al Zimmermann.

The Discussion Group

If you think you might enter the contest, you should join the contest discussion group. You can join either by sending a blank email here or by visiting the group on groups.io. The discussion group serves two purposes. First, it allows contestants to ask for clarifications to the rules. Be aware that sometimes these requests result in changes to the rules, and the first place those changes are announced is in the discussion group. Second, the discussion group allows contestants to interact with each other regarding programming techniques, results and anything else relevant to the contest.

My Lawyer Would Want Me To Say This

I reserve the right to discontinue the contest at any time. I reserve the right to disqualify any entry or entrant for any reason that suits me. I reserve the right to interpret the rules as I see fit. I reserve the right to change the contest rules in mid-contest. In all matters contest-related, my word is final.

Frequently Asked Questions

  • Can teams enter the contest?

    Yes. But a team can only be formed by those who have not already entered the contest as individuals. Once you enter as an individual, team membership is no longer open to you. Likewise, once you've joined a team you can't resign from it and start submitting grids on your own behalf.

    If you would like to form a team, please follow these instructions:

    • If they do not already exist, create individual accounts for each team member. Do not create a second account for any team member who already has one.

    • Let me know each team member's name and registered email address. It is important that no team member submit any entries to this contest until I notify you that the team has been created.

    • After I've created the team, team members can submit entries to the contest from their individual accounts. The contest engine automatically intercepts these entries and diverts them to the team account. The team is listed on the standings page.

    • Unless you are satisfied with the defaults, also let me know what team name and team location you would like to use on the standings page. Note that if all team members are from the same organization, the organization name can be included in the location, e.g., "Olaf Academy, Oslo, Norway".
      – For name, the default is "last-name-1 / last-name-2 / ... / last-name-n". For example, "Newton / Leibniz".
      – For location, the default is the smallest geographic entity containing all team member locations. For example, "Western Europe".

    Note: Teams are contest-specific. Joining a team for this contest does not affect your participation in other contests.

  • May I write a program that submits entries by bypassing my browser?


  • May I programmatically download the standings page at regular intervals? How frequently would be reasonable?

    Yes, you may programmatically download the standings page at regular intervals. Please feel free to download it as often as once per second. If you want to download the standings page more frequently than that, please contact me first.

  • What topics are appropriate for the discussion group?

    With only one exception, if it's related to AZsPCs then it's fine to talk about it in the discussion group. The exception is spoilers. Spoilers include:

    • specific solutions
    • detailed algorithms

    If you are not sure if something would be considered a spoiler, ask me.