Each of 16 individuals is to be given an identifying code consisting of one or more distinct digits in ascending order. What is the minimum number of distinct digits needed to give each individual a unique code?
Options:
A) 3 B) 4 C) 5 D) 6 E) 7
TWO WAYS-   1) we can do by looking at choices too   3-digits   since 3 is the lowest lets see how many can be nad ewith 3..   1) single digit - 3   2) 2 digits - different digits - 3*2/2 = 3.... 12,13,23   3) 3-digits - 123 - only 1   total = 3+3+1 =7...   4-digits   1) single digit - 4   2) 2 digits - different digits - 4*3/2 = 6.... 12,13,14,23,24,34   3) 3-digits - 4*3*2/3! = 4   4) 4-digits - 4*3*2/4! = 1   Total = 4+6+4+1= 
<gadget id="calculator">4+6+4+1</gadget>
<output>15</output>
15   so 5 should be the answer   ANSWER:5
<result>C</result>
Each of 16 individuals is to be given an identifying code consisting of one or more distinct digits in ascending order. What is the minimum number of distinct digits needed to give each individual a unique code?