Enigma 1364: Four all
15 December 2013
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From New Scientist #2523, 29th October 2005
I have in mind four numbers, each of four different digits one of which is 4. For each of them, four of the statements below are true and four are false.
(1) The number is a fourth power.
(2) The number is divisible by four.
(3) The number consists of a two-digit square followed by a smaller two-digit square.
(4) The product of the four digits exceeds the fourth power of 2.
(5) The number does not have two or more different prime factors.
(6) Each of the four digits is a perfect square.
(7) The digits form an arithmetic progression.
(8) The sum of the digits is prime, or else the sum of the two digits of that sum is 4.
What are my four numbers?
This is a similar type of problem to Enigma 1775.