We are looking for a three-digit integer in the decimal number system, which has the following properties: if the digits in the tens and units place are swapped, the sought number is obtained when written in octal (base-8); if the digits in the hundreds and tens place are swapped, a number is obtained which, when read in base-6, is 16 less than the sought number; finally, by swapping the digits in the hundreds and units place, a number in base-4 is obtained which is 18 greater than the sought number.