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I have a paradox: EIGHTY is a six digit number with no repeating digits and no zeros. When divided by 19, 17, 13, 11, or H, the remainders are, respectively, 17, 13, 11, 7 and G.
TWENtY is (another) six digit number with no repeating digits and no zeros (and uses a different key to EIGHTY above). When divided by T, perfect square WE or perfect cube NtY, the remainder is zero.
Find EIGHTY TWENtY
My interpretation is: The question requires a fractional base system converion e.g. 20 converted to base 2 is and 0010100 and 20 converted to base 1.6 is approximately 1001001.2589 which is a six digit number but both have repeating digits and zeros.
I could find TWENtY = 349125. Since WE is perfect square, it belongs to set: {25,36,49,49,64,81} and NtY is perfect cube, it belongs to set: {125,216,343,512,729}. Now, using the given information of no repeating digits, no zeros and the remainder, we can make combinations of WE and NtY to find TWENtY. I could not find EIGHTY, but I have a question here. Are the digits 'T','E','Y' in TWENtY the same as that in EIGHTY ?