With the given clues, let the digits of the 5-digit number be: abcde
i) Since, the number consists of 3 different digits, it means that either two of digits are repeated twice each or one of the digit is repeated thrice.
Then the digits could be: abbcc or abccc
ii) Since all digits are even numbers greater than 0, this means that the possible digits are 2, 4, 6 and 8.
iii) Since the value of the ones digit is 1/10 the value of the tens unit, this means that the tens place and the ones place have the same digit.
Thus, the number could be: abbcc
iv) Since the value of the tenth digit is 10 times the value of the 100th digit, this means that the required number has a decimal point and the first two digits after the decimal point are the same.
Thus, the number could be: abb.cc
v) Since the sum of the tenth digit and the hundredth digit gives you the hundreds digit. Recall that the tenth digit and the hundredth digit are the same.
Thus, the possible value for the tenth, hundredth and hundreds digits respectively are: 2, 2, 4 or 4, 4, 8
vi) Since the sum of the tens digit and the ones digit gives you the tenth digit. Recall that the tens digit and the ones digit are
the same.
Also, recall that the possible value for the tenth digit from condition (v) is 2 or 4. Then the value of the tens and ones digits is 2 while the value of the tenth digit is 4.
Having applied all the above conditions, therefore, the required 5-digit number is 822.44
Part B:
We know that the number we got in part A above is the only five digit number that satisfy the clues because, there is no other combination of digits that satisfies the given clues.
