Multimagic square
In mathematics, a P-multimagic square (also known as a satanic square) is a magic square that remains magic even if all its numbers are replaced by their kth powers for 1 ≤ k ≤ P. 2-multimagic squares are called bimagic, 3-multimagic squares are called trimagic, 4-multimagic squares tetramagic, and 5-multimagic squares pentamagic.
Trimagic square
A trimagic square is a magic square that remains magic when all of its numbers are replaced by their cubes.
Trimagic squares of orders 12, 32, 64, 81 and 128 have been discovered so far; the only known trimagic square of order 12, given below, was found in June 2002 by German mathematician Walter Trump.
Walter Trump (born 1953[1]) is a German mathematician and retired high school teacher. He is known for his work in recreational mathematics.
He has made contributions working on both the square packing problem and the magic tile problem. In 1979 he discovered the optimal known packing of 11 equal squares in a larger square,[2] and in 2003, along with Christian Boyer, developed the first known magic cube of order 5.[3] In 2012, Trump et al. described a model for retention of liquid on random surfaces.[4] In 2014, he and Francis Gaspalou were able to calculate all 8 × 8 bimagic squares.[5]
Until he retired in 2016, Trump worked as a teacher for mathematics and physics at the Gymnasium in Stein, Bavaria.
External links
- Walter Trump's pages on magic series
- Walter Trump's listings on the OEIS
- Walter Trump's solutions for one of Martin Gardner's puzzles
See PDF for complete article, downloaded:
Sunday, April 26, 2026 06:12PM