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Home»Math»2024 in math puzzles. – Math with Bad Drawings
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2024 in math puzzles. – Math with Bad Drawings

adminBy adminJuly 22, 2025221 Comments5 Mins Read22 Views
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2024 was a good year to do math puzzles. Can you guess why?

Easy: because the last 100,000 years have all been good years to do math puzzles.

But this year was especially good, because it saw the publication of (at least) three fabulous new books of mathematical challenges, games, and provocations.

From the inimitable (and inimitably punctuated) Gord! comes this collection of fourteen open-ended math puzzles. Each gives a kind of mechanism or guiding rule, which then lends itself to myriad (nay, infinite!) avenues of exploration.

Here’s the first (lightly paraphrased):

Write the numbers 1 to 25 in a 5-by-5 grid. Now drop a hungry bug on one of the squares. It eats that number, then moves up, down, left, or right to the lowest adjacent number, where it eats again, repeating this process until it can move no further.

Which starting numbers will allow the bug to traverse the whole grid?

(Example: if the bug starts on 14, it will not traverse the whole grid. It misses the bottom row.)

These “pickles” stretch the “low floor, high ceiling” concept to extremes. That is, they lead quickly into unsolved research problems (What about larger grids? What about rearranging the numbers? What if the grid is an arbitrary graph?), and also, they appeal to my five-year-old.

In other words: the floor is in Earth’s mantle, and the ceiling is in the stratosphere. Perfect for the math teacher in your life.

“Playful, eclectic, and ingenious,” is the unsolicited blurb I offered in an email; “in short, it’s unmistakably Walter.”

On second thought, I might call it “a museum of an irreplaceable mind.”

The book collects 239 emanations of what I call Joris Radiation. That includes two-player games, paper-folding activities, prompts for improvisation, and mathematical provocations (much in the spirit of Gord!’s pickles).

For example: If you draw a bunch of cross-shaped pentominos on graph paper, what’s the largest gap you can create, such that no cross can fit in the gap?

Or, for another: Write a string of digits. Then, remove any pair of digits, and replace them with the digits in their sum; for example, 9 and 9 can be replaced with 1 and 8. Repeat this process as long as you like. (Also, since zeros don’t affect sums, you may just leave them out.)

When is it possible to reduce the number string to nothing but 1’s?

It can take some work to decipher Walter’s instructions, and to distinguish the costume jewelry from the priceless gems. But if you want to swim in the stream of a bizarre and fabulous consciousness, you can do no better. Perfect for the creative weirdo in your life.

I’m not quite sure how to describe this book, so let me deploy one of the devices Bellos puts to great effect in the book: multiple choice. Is this book most appealingly described as…

1) A light, snackable compendium of puzzles requiring no special knowledge or expertise?

2) A curiosity-widening volume of puzzles drawn from various disciplines: probability, geography, logic, physics, game theory, and most delightfully, cognitive psychology?

3) A provocative collection of puzzles where your fiercest intuitions will betray you?

4) Another fabulous puzzle book from Alex Bellos, who is making a real habit of such things?

Over in his puzzle column at The Guardian, Alex has given some puzzles in the same style, and a couple from the book itself. Great for the Sudoku fan, the crossword fan, or just the fan of intellectual surprises and “ooh!” moments.

Not in the habit of buying books, I see? But you are in the habit of clicking hyperlinks? Well, I can’t endorse your lifestyle, but I can’t judge either; my own hyperlink-to-book ratio is functionally infinite.

Anyway, you’ll enjoy Tanya’s blog, which featured some classically elegant puzzles in 2024:

Great as those are, I was even more fond of Tanya’s open-ended “lateral thinking” puzzles (and the wonderfully varied answers Tanya’s students gave). In addition to heavy thingy and home late, here are three of my favorites:

Thrice makes sixty:

I can use the number 20 thrice to make 60: 20 + 20 + 20 = 60. Make 60 again by using a different number three times.

Clean sister, dirty sister:

One day, two sisters decided to clean the old shed at the bottom of their garden. When they finished cleaning, one had a dirty face and the other had a clean face. The sister with the clean face went and washed her face, but the girl with the dirty face did not wash. Why should this be so?

And my personal favorite, guessing the number in one question:

Mike thought of one of three numbers: 1, 2, or 3. He is allowed to answer “Yes”, “No”, or “I don’t know”. Can Pete guess the number in one question?

Puzzles with Bad Drawings

What about here, at this very blog? Well, I am pleased to highlight the lovely job my pal Chris did in creating the daily information-gathering puzzle L.A.P.

But also, this year’s posts included:

And I’ve started closing out my monthly roundup posts with a “parting puzzle.” They’re collected here (with spoilers). And while I’m at it, here’s one for this month, slightly different in flavor…

A Parting Puzzle: The Divided States of Economica

Fact: the U.S. has the world’s largest economy (as measured by GDP).

But let’s break the U.S. into smaller economies, and see how much of the world’s Top 10 it can thereby dominate.

(1) Warm-up: Treating the U.S. as 51 separate economies, one for each state (plus DC), how many rank among the world’s ten largest?

(2) Challenge: Now, consider all the ways to decompose the U.S. into new, smaller economies, each consisting of one or more contiguous states. Let’s do this to maximize the number of economies that rank in the world’s ten largest. What’s the best you can do?

Here’s a csv to get you started:

Like this:

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  198. ラブドール セックス
    ラブドール セックス on September 21, 2025 4:46 pm

    オナホ フィギュア55 Wellhonored weapon; the worm was slaughtered.The great one had gained then by his glorious achievement To reap from the ringhoard richest enjoyment,

    Reply
  199. ラブドール
    ラブドール on September 21, 2025 4:54 pm

    ラブドール 女性 用said that theprince was at home,and showed him into a clean little anteroom.

    Reply
  200. リアル ラブドール
    リアル ラブドール on September 21, 2025 4:59 pm

    up to the point which produces the largest amount of revenue(supposing that the State needs all the revenue which it yields) is notonly admissible,but to be approved of.フィギア エロ

    Reply
  201. ラブドール セックス
    ラブドール セックス on September 21, 2025 5:08 pm

    Far as I canmake out from her story,エロ フィギュア 無 修正Phillips has been carrying matters witha rather high hand.

    Reply
  202. ラブドール 高級
    ラブドール 高級 on September 21, 2025 5:19 pm

    Marilla? Allan told me she was a dunce at geometry too.エロオナホYou don’t know how thatencouraged me.

    Reply
  203. リアル ラブドール
    リアル ラブドール on September 21, 2025 5:30 pm

    and waited for the wordof judgment.高級 オナホThere was no mistaking her sincerityit breathed in every tone of hervoice.

    Reply
  204. 高級 ラブドール
    高級 ラブドール on September 21, 2025 5:49 pm

    ラブドール 激安who was in the lead,finally discovered a big tree withsuch widespreading branches that there was room for the party to passunderneath.

    Reply
  205. ラブドール セックス
    ラブドール セックス on September 21, 2025 6:00 pm

    フィギュア 無 修正and if” my friend,” she interrupted.

    Reply
  206. リアル ラブドール
    リアル ラブドール on September 21, 2025 6:09 pm

    The reason fornot interfering,unless for the sake of others,フィギア エロ

    Reply
  207. ラブドール 高級
    ラブドール 高級 on September 21, 2025 6:21 pm

    エロオナホand the bakingpowder biscuits which Marilla will make justbefore teatime.I assure you,

    Reply
  208. ラブドール
    ラブドール on September 21, 2025 6:33 pm

    オナホ フィギュアlimiting ‘sweord’; the latter as an adj.c.

    Reply
  209. ラブドール セックス
    ラブドール セックス on September 21, 2025 6:55 pm

    フィギア エロand in a minor degree,society atlarge.

    Reply
  210. ラブドール 高級
    ラブドール 高級 on September 21, 2025 7:09 pm

    ”“It’s very naughty of you to speak so about Mr.エロオナホBell,

    Reply
  211. 高級 ラブドール
    高級 ラブドール on September 21, 2025 7:29 pm

    When she reached William Bell’s field she fled across it as if pursued by an army ofwhite things,エロ フィギュア 無 修正and arrived at the Barry kitchen door so out of breaththat she could hardly gasp out her request for the apron pattern.

    Reply
  212. ラブドール
    ラブドール on September 21, 2025 7:41 pm

    高級 オナホthere are a lot morecherrytrees all in bloom! This Island is the bloomiest place.I justlove it already,

    Reply
  213. リアル ラブドール
    リアル ラブドール on September 21, 2025 7:52 pm

    ” said Marilla grimly,remembering the success of this method in the former case.エロ フィギュア 無 修正

    Reply
  214. 高級 ラブドール
    高級 ラブドール on September 21, 2025 8:01 pm

    ラブドール 激安and at once thegreat assemblage hushed as if by magic.The biggest of the tigers cameup to the Lion and bowed,

    Reply
  215. ラブドール 高級
    ラブドール 高級 on September 21, 2025 8:11 pm

    } 45 Dared to adventure to look at the woman With eyes in the daytime;6 but he knew that deathchains Handwreathed were wrought him: early thereafter,When the handstrife was over,オナホ フィギュア

    Reply
  216. リアル ラブドール
    リアル ラブドール on September 21, 2025 8:25 pm

    EARNobleman,any brave man.ラブドール 激安

    Reply
  217. ラブドール セックス
    ラブドール セックス on September 21, 2025 8:36 pm

    ラブドール 女性 用sat beside him,and her face certainly was both triumphantand taunting.

    Reply
  218. 高級 ラブドール
    高級 ラブドール on September 21, 2025 9:02 pm

    The pledge that he made theeBreca outdid you entirely.オナホ フィギュア The son of Beanstan hath soothly accomplished.

    Reply
  219. リアル ラブドール
    リアル ラブドール on September 21, 2025 9:19 pm

    Royalty payments must be paid within 60 days following each date on which you prepare (or are legally required to prepare) your periodic tax returns.ラブドール 激安Royalty payments should be clearly marked as such and sent to the Project Gutenberg Literary Archive Foundation at the address specified in Section 4,

    Reply
  220. リアル ラブドール
    リアル ラブドール on September 22, 2025 12:01 am

    is bound up with all itsfathomless joy,ラブドール 女性 用all its torturing agonies in his bosom.

    Reply
  221. ラブドール
    ラブドール on September 23, 2025 4:21 am

    made me an offer,ドール エロMamma! Mamma! ?she exclaimed.

    Reply
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