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Magic square
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===Parker square=== The '''Parker square''', named after recreational mathematician and maths YouTuber [[Matt Parker]],<ref>{{cite arXiv|eprint=1908.03236|quote=Some ’near misses’ have been found such as the Parker Square [2] |last1=Cain |first1=Onno |title=Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares |date=2019 |class=math.RA }}</ref> is an attempt to create a 3{{resx}}3 magic square of [[Square number|squares]] — a prized unsolved problem since [[Leonhard Euler|Euler]].<ref>{{cite web|last1=Boyer|first1=Christian|title=Latest research on the "3x3 magic square of squares" problem|url=http://www.multimagie.com/English/SquaresOfSquaresSearch.htm|website=multimagie|access-date=16 June 2019|quote=The two corresponding prizes are still to be won!}}</ref> Discovered in 2016, the Parker square is a trivial semimagic square, since it uses some numbers more than once, and the diagonal {{math|23{{sup|2}} + 37{{sup|2}} + 47{{sup|2}}}} sums to {{val|4107}}, not {{val|3051}} as for all the other rows and columns, and the other diagonal. A true 3{{resx}}3 magic square of square numbers has to date not been discovered (despite computer searches). In a ''[[Numberphile]]'' video from June 2023, Mathematician Tony Várilly-Alvarado used mathematics to speculate that the existence of such a square is "probably impossible".<ref>{{Cite AV media |url=https://www.youtube.com/watch?v=Kdsj84UdeYg |title=Magic Squares of Squares (are PROBABLY impossible) - Numberphile |date=2023-06-13 |last=Numberphile |access-date=2025-03-05 |via=YouTube}}</ref> In February 2025, Parker upped his years-old bounty of US$1,000 to $10,000 to find a fully magic 3{{resx}}3 square using square numbers.<ref>{{Cite AV media |url=https://www.youtube.com/watch?v=stpiBy6gWOA |title=A Magic Square Breakthrough - Numberphile |date=2025-02-09 |last=Numberphile |access-date=2025-03-05 |via=YouTube}}</ref> {| class="wikitable" style="margin-left:auto;margin-right:auto;text-align:center;table-layout:fixed;width:8em;height:8em;" |- | 29{{sup|2}}|| 1{{sup|2}}|| 47{{sup|2}} |- | 41{{sup|2}}|| 37{{sup|2}}|| 1{{sup|2}} |- | 23{{sup|2}}|| 41{{sup|2}}|| 29{{sup|2}} |}
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