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by BRG on August 26, 2019

New Scientist Enigma 514 – State of the Parties

by Ian MacKillop

From Issue #1666, dated May 27, 1989

I wrote to a mathematician friend in Utopia and asked him to send me the results of the recent general election there. He decided to make me work for it, as you can see from his reply:

“Dear Friend,

  1. The Dextrous Party lost control of the Scitting (our 600-seat parliament) and now has fewer seats than the Sinistrals. The Other and Indeterminate parties remained third and fourth respectively;
  2. No new party was elected to the Scitting and none was removed;
  3. No party has an overall majority in the new Scitting;
  4. The Other Party lost almost half its seats, while the Indeterminate Party exactly doubled its seats;
  5. In the last Scitting all four parties held a perfect square of seats (the Other’s figure was also a perfect cube). In the new Scitting, two have perfect squares while the other two have perfect fifths (a whole number raised to the fifth power). No party had or has only one seat.

So now you can determine the composition of both old and new Scittings.”

Can you?

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