ITPEC FE Morning October 2018 Question 25
Currently, the number of customers is 8,000 with annual increase rate of 20%. By assigning a fixed length code using 26 uppercase alphabet A- Z to each customer, what is the minimum code length required to accommodate all the customers for next three years?
Explanation
3 characters — find the customer count after three years, then the shortest length n with 26n at least that large.
- •Customers after three years of 20% growth: 8,000 × 1.23 = 8,000 × 1.728 = 13,824
- •Two letters give 262 = 676 codes, far too few
- •Three letters give 263 = 17,576 codes, and 17,576 ≥ 13,824
Answer (a)
Why not others:
- •(b) 4 — 264 = 456,976 codes is enough, but three characters already suffice, so it is not the minimum
- •(c) 5 and (d) 6 — 265 and 266 give millions of codes, far beyond 13,824; they are also sufficient but not the shortest length
Key rule: A fixed-length code over an alphabet of k symbols with n positions has kn values; pick the smallest n that covers the largest future count.
Basic Theory · AI-written, may contain errors
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