120年謎の難問パズル解明　「悪魔の証明」に日米の数学者が挑んだ

US-Japan team of mathematicians has solved an over 120 year-old puzzle through the use of the "Devil's Proof"

石倉徹也

ISHIKURA, Tetsuya

2025年3月10日 15時00分

120年以上謎だった難解パズルを解明したと、日米の数学者3人が10日、発表した。「悪魔の証明」とも言われる「ないことの証明」に成功しており、計算機で解くことが困難な図形パズルに新たな解法が得られる可能性がある。

A team of mathematicians from both the U.S. and Japan has announced on the 10th that they've solved an over 120 year-old puzzle, which upon showing that an equilateral triangle could be cut into four pieces to form a square in 1902, posed the question of whether or not three pieces or lower could be cut to form a square.

The team successfully solved it using what is known as the "Devil's Proof," by proving that "a square could no longer be formed." From this, it's now possible to obtain new techniques from geometry-based puzzles that are difficult for computers to solve.

　証明したのは「正三角形を3ピースに分解して、裏返さずに並べ直して正方形を作ることは不可能」という定理。論文が昨年12月、査読前のプレプリントとして「arXiv」に投稿された（https://doi.org/10.48550/arXiv.2412.03865別ウインドウで開きます）。

The team proved the theorem that "Dividing a triangle into three pieces, and lining them up to form a square without flipping any over isn't possible." The pre-reviewed publication was posted on arXiv in December of last year.

More ...

## REFERENCE

オンラインカジノ会社の広告、問題ないの？　お金賭ければ違法だけど

Having problems with online casino commercials? They're illegal if you make money

御船紗子 後藤遼太

MIFUNE, Saeko; GOTO, Ryota

2025年3月4日 11時00分

　ネットでスポーツ中継を見ていたら、オンラインカジノの運営会社の広告が流れてきた。日本では公営以外の賭博は違法なはずなのに、問題はないのか。

If you watch sports broadcasts online, you'll find that there are commercials from online casinos that come out. In Japan, other than state-run casinos, these are supposed to be illegal.

　サッカーやプロ野球などスポーツ動画を配信する「DAZN」では、試合中継の合間にオンラインカジノ最大手「ベラジョン」などの広告を流してきた。

One case for example is "DAZN," which broadcasts sports videos of soccer and professional baseball matches. The company had shown ads from giant online casino company "Vera&Jon" during break intervals of the matches.

　実は、流れているのは、お金を賭けない「無料版ゲーム」の広告。ベラジョン無料版のサイトには、「超画期的なオンラインカジノ」「完全無料で楽しめちゃいます！」とある。

Actually, what they showed was a commercial of the "free version of the game" where a person won't make money. In the website of the free version of Vera&Jon, there are words like "Super Impressive Online Casino," "Let's enjoy completely free online casino!"

　消費者庁によると、たとえ「カジノ風」でも、お金を賭けなければ「あくまでゲーム」とみなされるという。

According to the Bureau of Consumer Affairs, even if "casino is used as the theme," people would consider the app as "only a game" if no money can be earned.

　DAZNジャパンは取材に、「無料版であること、違法の有料版に誘導されないことを前提に放映してきた」と回答。一方、「現在は基準見直しのため、配信はストップしている」という。

DAZN Japan responded, "For the free version, the commercials were shown with the premise that viewers would not be led to the paid version, which is illegal. Right now, we've stopped broadcasting the commercials to allot time for the rules to be reviewed."

「射幸心をあおらない」からOK？　いまは見合わせ

It's OK if "gambling is discouraged?"

　テレビなどでも問題になっている。

The ads have become a problem even on TV, among others.

　テレビ朝日は2月25日の定例会見で、ベラジョン無料版の広告を2022～23年に放送していたと説明。「有料版に誘引しない、射幸心をあおらない」などの基準を満たしていたが、「総合的に判断し」、放送を見合わせたという。

TV Asahi explained in a meeting in Feb. 25 that the commercials of the free version of Vera&Jon were broadcasted from 2022 to 2023. While the commercials did fulfill basic precepts like "Not to lead viewers to the paid version," its broadcasts have been suspended after a "unanimous decision."

　BSテレビ東京は、20～23年にベラジョンと「ミスティーノ」、BS―TBSが21～23年にベラジョンと「遊雅堂」無料版の広告を放送したと公表。ニッポン放送も無料版の広告の「放送の実績がある」と発表した。

BS TV Tokyo has said that it broadcasted the commercials of Vera&Jon and "Mystino" in 2020 to 2023, while BS-TBS said that it broadcasted the free version of "YU-GA-DO" and Vera&Jon from 2021 to 2023.

　サッカーJ2の北海道コンサドーレ札幌は、無料カジノゲームサイトの運営会社とのスポンサー契約の見直しを含めて検討中だ。

Soccer J2's Hokkaido Consadole-Sapporo is currently examining the operations of free casino gaming sites, including reviewing their terms of sponsorship.

　オンラインカジノの多くは、マルタやオランダ領キュラソーなどで登録され、「合法」とうたう。しかし、日本では競馬や競艇など法律で認められた公営ギャンブル以外でお金を賭ける行為は違法になる。日本からアクセスして賭ければ刑法の賭博罪が成立。罰則は50万円以下の罰金で、「常習賭博」の場合は3年以下の懲役だ。

Many of the online casinos are registered in Malta and Curacao in Holland, where they are "legal." However, in Japan, the law on horse and boat racings says that they are illegal if they are not state-run and people can make money. There's a prison sentence for violations related to gambling if these online casinos are accessed from Japan and people make money. The punishment is under 500,000 yen, while the sentence is under three years for "habitual gambling."

薬物なら広告も違法、オンラインカジノは?

If the ads online were for medicines, they'd also be illegal. What about for online casinos?

Regarding the ads, in the case of medicines, they would be illegal according to the Stimulants Control Act and Medical Devices Act (Pharmaceutical Devices Law), among others. However, according to the Ministry of International Affairs and Communications, there's no rule against online casinos, which include their paid versions. A spokesperson says, "Even if it was a free version that leads to the paid version, which in turn can be linked to a gambling addiction, it's not illegal. However, it is 'harmful information.'"

Even Comedian Mr. YOSHIMOTO says, 'Since it had ads on the Internet..."

There are also cases where the commercials became the "entry point."

In November of last year, there was an incident where the police investigated the documents of 10 people suspected of gambling in an online casino. A 40-year-old male from downtown stated, "I found the ads online."

Another incident involved Mr. TAKAHIRA, Kuruma, the "Reiwa Romanticist" comedian, who was reported to have used an online casino, and who said in an apology video that "he didn't find the ads illegal given that they also appeared online."

Professor Emeritus TORIHATA, Yoichi (Financial Theory) from Shizuoka University is knowledgeable about the situation, and has pointed out, "The logic that it's a free version, so it has no connection with the paid version is a difficult problem." For example, when we see Vera&Jon's commercial of the free version, and searched it using our smartphone or PC, what comes out at the top of the list is the site of the paid version.

Online casinos don't need to have an establishment, and since people can easily register, businesses are in a disarray, putting money into the ads to acquire clients. Prof. TORIHATA checked a number of sites of the free version, and explained the gist of the terms of usage, "The data collected are used for market research and for soliciting clients to play the game or use the service." He says, "Playing the free version lowers the hurdle to play the paid version." For businesses that want to increase new user registrations, the free version's information of its registered users is invaluable. It's also highly likely that the information will be further used for their marketing campaigns, hence we must not see the app as safe just because it's free."

"The risk of gambling addiction is high"

In "A Community that Thinks about the Gambling Addiction Problem," Ms. TANAKA, Noriko said that she feels that consultations on how to make money are increasing due to the free version.

She pointed out, "There are plenty of people, mainly young people, who've gotten used to paying money in a smartphone game. It's in this same sense that people enjoy the free version. There are also examples of people being led to an illegal site without being aware of it. Thus, media and the influencers, among others, who show the ads have a big responsibility."

Consultations related to online casinos that her group visited increased rapidly after the COVID-19 of 2021. Before the COVID-19 in 2019, only eight cases were reported for the whole year. In 2023, there were 97.

If you have a smartphone, it's available 24 hours and for 365 days, so the risk of addiction is also high. Recently, it has spread to even high school students, among many others who are in their tens. "The money that can be borrowed by young people isn't much. This is why there are also people who join sketchy part-time jobs. It would be a huge problem if people do this just for fun."

## REFERENCE

（天声人語）ともだち１００人できるかな

VOX POPULI: I wonder if I could make a hundred friends

2025年3月4日 5時00分

　小学校へあがる直前に引っ越した。一緒に遊んだみんなと別れ、違う学校へ。いまはふてぶてしい中年にも、繊細な幼少期はあったのだ。だから、あの歌には感ずるところが多かった。まど・みちおさんの作詞である。〈一ねんせいに　なったら／ともだち　ひゃくにん　できるかな〉▼

We moved just before I went to grade school. I left everyone whom I played with and transferred to a different school. Now, even at middle age, I thought that it was a precarious time for me in kindergarten. This was why I had been rather sentimental toward that song whose lyrics were written by Mr. Michio Mado. (When I get to grade 1, I wonder if I could make a hundred friends)

What kind of place is a school? I wondered if I could do well. I turned the worries that I felt into excitement, expanding my horizon. Even the magazine from grade school, "Grade 1," was among those who gave me encouragement. This year, I heard that it would be its 100th anniversary since its founding, a publication whose history began since before the war. Its latest April issue came into my possession only after a long while.

Flipping through the pages, I found that there was a section with a quiz that went well with the current programming classes in school. Or so I thought, because Nobita and Doraemon were playing as usual together with everyone at the vacant lot where the concrete pipes were. It was a special feature that presented life at the school, where picnics and such things took place while children smiled brightly.

I was happy to make a lot of friends. It would surely be fun to be able to eat onigiri rice balls at the top of Mount Fuji. But we should be careful, wrote Mr. Mado in a poem called "The Beautiful Word."

(Enjoy saying it. The beautiful word, 'Friend,' whose meaning we give: Let's pretend we don't know those who are not our friends.)

I wondered if the assumption was that we must use our friends as a means to justify the distinction. It was an important message for children, even for adults.

## REFERENCE

「毒」から逃げろ、がん転移の始まりの一端を解明　京大がマウス実験

Run-away from "Poison!" Kyoto University explains the start of cancer metastasis through mice experimentation

桜井林太郎

SAKURAI, Rintaro

2025年3月3日 10時01分

日本人の死因トップのがん。治療でとりわけやっかいなのが、がんが最初にできたところからほかの臓器・組織に移る「転移」だが、実はなぜ転移するかはよくわかっていない。京都大や名古屋大の研究チームは、がん組織内には、活性酸素種の一つ、過酸化水素が高濃度に蓄積する「ホットスポット」が存在し、そこから逃げるようにがん細胞の一部が分離、放出されることで転移が始まるとマウス実験で突き止めた。

Cancer is the leading cause of death for Japanese people. But what is especially perilous during medical treatment is that it's actually not very well-understood why cancer cells transfer to other organs from where they were first produced, or what is known as "Metastasis." The research team comprised of Kyoto University and Nagoya University have hit on a discovery while experimenting with mice, showing that within a cancer group, there exist one of the reactive oxygen species (ROS) and a "hotspot" that accumulates hydrogen peroxide in a high degree of density, and that it is from there that a portion of cancer cells separate, as they try to escape and get out, hence starting the metastasis.

　研究成果が英科学誌ネイチャー・セル・バイオロジーに掲載された。

The results of the research have been published in the English science magazine, Nature Cell Biology.

　ヒトを含む多くの生物は酸素を利用してエネルギーを獲得するが、と同時に活性酸素種が生体内にできる。活性酸素種が蓄積すると酸化ストレスが生じて細胞を傷つけるため、多くの細胞にとって毒ともいえる存在だ。がん組織は代謝異常などによって活性酸素種が特に蓄積しやすく、とりわけ強い酸化ストレスにさらされているとされる。

While living things, including humans, use oxygen to obtain energy, they also produce reactive oxygen species within their bodies at the same time. When reactive oxygen species accumulate, oxidative stress is produced and harm the cells. This, for many of the cells, can be poisonous. A cancer group can accumulate these reactive oxygen species easily through metabolic disorder, among others, and further increase oxidative stress.

　研究チームは、1個の細胞レベルで外部の活性酸素種を直接的に検出する手法を開発。ヒトのがん細胞を移植したマウスで、がん組織の内部を観察したところ、過酸化水素の分布は不均一で、濃度が局所的に高いホットスポットが存在。その部分にさらされたがん細胞ではがん組織から分離、放出されることが活発に起きていた。関連する遺伝子の働きからも確認された。

The research team has developed a way to directly detect foreign reactive oxygen species at the cellular level per cell. In the mouse where a human cancer cell was transferred, the distribution of hydrogen peroxide was found to be uneven when the cancer group was observed. Moreover, they found that there was a high-density hotspot inside. The cancer cells that were exposed to that part became eager to get out, and eventually separated from the cancer group. This observation has also been verified in the function of related genes.

　さらに詳しく調べると、免疫細胞の一種である好中球がこのホットスポット周辺で集まっていることも観察された。好中球をがん組織から取り除くと過酸化水素のホットスポットがつくられにくくなった。

Upon further investigation, the neutrophil, a type of immune cell, was also observed to gather around this hotspot. When the neutrophils are removed from the cancer group, it became harder to create the hydrogen peroxide hotspot.

　これらのことから、がん組織に集まった好中球が過酸化水素をつくってホットスポットを形成し、それにさらされたがん細胞が有害な過酸化水素から逃げるように分離、放出されることで転移が始まると考えられるという。

From this, it was learned that the neutrophils that gathered in the cancer group created the hydrogen peroxide and formed the hotspot. The cancer cells that were exposed to this hotspot separated in their attempt to escape from getting harmed by the hydrogen peroxide. This is considered to be what starts the metastasis.

Among the variety of cancer cells, there's also a type that is strong and has an anti-oxidization effect, which hinders the functionality of the reactive oxygen species. These cancer cells were found to have the tendency to be a lot harder to separate and get out.

The research team used this mechanism to develop a drug to control this transfer (metastasis) by removing only the reactive oxygen species that become the cause for the separation and the release of cancer cells to other organs.

Assoc. Prof. Takahashi, Shigenari of Kyoto University (Medical Chemistry) says that "to escape" is the most fundamental defense mechanism that any living thing has, yet he was surprised to find out that the cancer cells were also fleeing. He said, "If an environment where there won't be a need for cancer cells to 'escape' could be created, it would be possible to prevent metastasis from occurring."

The abstract of the publication can be found here: https://doi.org/10.1038/s41556-025-01617-w

## REFERENCE

（社説）高額療養費　「その場しのぎ」の限界

Community Discussions: The limitation of "temporary answers" to high-costing medical treatment

2025年3月3日 5時00分

少子高齢化が進む中で、国民皆保険にどんな役割を担わせるべきなのか。社会全体が困難な選択に向き合い、熟議すべき大きなテーマだ。その場しのぎでは行き詰まる。中長期的に意味のある解決を目指すには、与野党が協議する場づくりが不可欠だ。

What type of role must the National Health Insurance take in the face of an aging population? This is a big topic that needs to be discussed, and where the whole community will have to make a difficult decision. It's here where we're stuck. In aiming to solve the problem in the mid-long term, it's necessary to create a venue where both the ruling party and the opposition can convene.

　医療費の患者負担に月ごとの上限を設ける「高額療養費制度」の見直しをめぐり、石破首相が政府案の再検討を国会で表明した。３段階で予定していた限度額引き上げのうち、今年８月の第１段階は実施するが、その後については今秋までに「改めて方針を検討し、決定する」という。

Concerning the revision to the "policy on high-costing medical treatment," which sets the maximum amount that the patient shoulders for medical treatment per month, Prime Minister ISHIBA has announced the re-evaluation of the said government policy during the National Assembly. The plan has been to raise the amount during the third stage, and that the first stage is to be implemented in August of this year, while during the fall of this same year, the policy is going to "be reviewed again to decide what happens afterward."

　その過程では、患者団体を含む関係者の意見を十分聞くというが、大きな影響を受ける当事者の声に耳を傾けるのは本来、当然のことだ。だが今回はこの点が全く足りず、患者団体や専門家から、制度見直しの進め方自体が拙速だと強い批判を受けている。

During this process, it's obviously important to listen to those who'll be greatly affected by the policy, and that the opinions of the stakeholders including the patients group are adequately heard. However, this part didn't turn out as well as it should in this case, and there's strong criticism from the patients group as well as the experts that the re-evaluation of the policy is being hurried.

　さらに気になるのは、首相が「増大する高額療養費を能力に応じてどのように分かち合うか」と述べたことだ。この制度の枠内でやりくりする前提にも聞こえるが、それでは解を見いだしにくい。より幅広い選択肢を並べて議論を深めるべきではないか。

What further needs to be emphasized is the question that the prime minister has raised: "How can the increasing cost of medical treatment be shared according to each person's capability?" While there appears to be a presumption to make ends meet within the bounds of the policy, it's difficult to find a solution. Wouldn't it be necessary to move forward with the discussions by listing a wider array of options?

　例えば、新年度予算案の修正で与党と合意した日本維新の会は、高額療養費の限度額引き上げには反対を表明する一方で、社会保険料の引き下げ策として、市販薬と効果やリスクが似る薬（ＯＴＣ類似薬）への保険給付を見直すことを重視している。

For example, while the Japan Restoration Party agreed with the ruling party to revise the budget for the new year, it expressed its opposition to increase the maximum amount that is shouldered by patients for high-costing medical treatment, and has been drawing attention to the re-evaluation of insurance payments, which cover over-the-counter medicines and those with similar effects and risks, in order to bring down the fees stipulated in the social insurance policy.

　高額療養費がカバーするのは、重い病気やケガの医療費で生活が破綻（はたん）しかねないような「大きなリスク」だ。それと比べれば、風邪薬や湿布など日頃使う薬の負担は「小さなリスク」かもしれない。ただ、より多くの人が恩恵を受けており、そこを削ることへの反発も予想される。

The high-costing medical treatment fees cover serious diseases and injury that are "big risks," because they could easily destroy a person's life. Compared to this, the cost of everyday medicines like those for colds or some kind of compress may be considered to be "minor risks." However, more people are benefiting from the latter that it's foreseen that taking away these from the current policy would lead to protests.

　教訓がある。立憲民主党の野田佳彦代表が首相だった民主党政権下の１１年、厚生労働省は、外来患者が受診のたびに窓口で１００円を上乗せして払う「受診時定額負担」を提案した。高額療養費の限度額引き下げのためだ。

There's a lesson to be learned during the time of Mr. Yoshihiko NODA of the Constitutional Democratic Party of Japan who served as the prime minister under the Democratic Party in 2011. The Ministry of Health, Labour and Welfare proposed adding 100 yen to the "fixed cost during diagnosis" that is paid when an outpatient comes for diagnosis. The objective was to lower the maximum amount shouldered by patients for high-costing medical treatment.

　だが、日本医師会が「受診控えを起こす」などと猛反発し、「低所得者ほど負担が重くなり、格差を助長する」といった批判も出て、民主党内もまとまらず見送られた。

However, the Japanese Medical Doctors Association heatedly protested that "it'll discourage patients from coming for diagnosis." It was also criticized for "increasing the cost shouldered by low-income patients, which in turn increase the income gap even further." The Democratic Party bid this farewell, without being able to find a resolution.

　ことほどさように、医療をめぐる負担と給付の合意形成は難しい。様々な利害にどれだけ多くの政治家が責任をもって向き合うのかが、解決へのカギを握る。今秋にとどまらず、その先も見据えた建設的な議論につなげるべきだ。

As time goes by, it's difficult to reconcile the cost of medical treatment and the amount to be paid. However, the key to solving the problem is found in the number of politicians who'll take responsibility for the various pros and cons of the policy. Before fall comes, it's necessary to have a constructive discussion on what is foreseen to lie ahead.

## REFERENCE