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Any parellogram would work since given four digit number n1n2n3n4, it is divisible by 11 iff n1+n3=n2+n4, and each ni is linear combination of the coords of key
by qrian 2y ago
Any parellogram would work since given four digit number n1n2n3n4, it is divisible by 11 iff n1+n3=n2+n4, and each ni is linear combination of the coords of keypads xi, yi, and thus (n1+n3)/2 = (n2+n4)/2
- sweezyjeezy 2y agoNice - the n1 + n3 = n2 + n4 equality is only necessary (mod 11) e.g. 9020 works - this is because 99...99 with even # of 9s is divisible by 11 and with odd # 9s is divisible by 11 if we subtract 9 (or add 2) so then is = -2 mod 11. So then for example with 4 digits 1000a + 100b + 10c + d = [a + b + c + d] + [999a + 99b + 9c] = [a + b + c + d] - 2a - 2c (mod 11) = (b + d) - (a + c) (mod 11)