TOKYO — As Japan ’s first female prime minister, Sanae Takaichi has broken new ground in a country that struggles with gender equality. But she has quickly run up against a tradition that may be immovable.

Trophies for sumo wrestling, Japan’s national sport, are sometimes presented by the country’s top leader — most recently in January, when Shigeru Ishiba , the prime minister at the time, awarded the winner’s trophy at the New Year Grand Sumo Tournament in Tokyo.

But awkward questions arose ahead of the Kyushu Grand Sumo Tournament, which concludes Sunday in the Japanese city of Fukuoka. Takaichi is prohibited from entering the ring according to the rules of sumo, which consider women impure.

Takaichi will have a chance to sidestep the issue as the Japanese leader is expected to

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