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In their book, Kathleen Ollerenshaw and David S. Brée give a method of construction and enumeration of all most-perfect magic squares. They also show that there is a one-to-one correspondence between reversible squares and most-perfect magic squares. For n = 36, there are about 2.7 × 10 44 essentially different most-perfect magic squares.
if the last digit of a number is 3 or 7, its square ends in an even digit followed by a 9; if the last digit of a number is 4 or 6, its square ends in an odd digit followed by a 6; and; if the last digit of a number is 5, its square ends in 25. In base 12, a square number can end only with square digits (like in base 12, a prime number can end ...
Since each 2 × 2 subsquare sums to the magic constant, 4 × 4 pandiagonal magic squares are most-perfect magic squares. In addition, the two numbers at the opposite corners of any 3 × 3 square add up to half the magic constant. Consequently, all 4 × 4 pandiagonal magic squares that are associative must have duplicate cells.
A list of articles about numbers (not about numerals). Topics include powers of ten, notable integers, prime and cardinal numbers, and the myriad system.
After all 100 spaces are filled, the digits 0 to 9 are randomly assigned to rows and columns. Payouts are based on the last digit of the score of each team at the end of the first quarter, half ...
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Primes p for which p − 1 divides the square of the product of all earlier terms ... are primes ending in the decimal digit d. 2n+1: ... 12 p − 1 ≡ 1 (mod p 2): ...
The Macy's Thanksgiving Day Parade is a perfect example. The 2024 parade reached 32 million viewers. ... Year-end inventories were up 2.5% year over year. Roughly half of the increase was due to ...