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 A prime time at KP (Posted on 2006-05-31)

Military time is based upon a 24-hour clock. The time is expressed in the form abcd hours where a, b, c, and d are base 10 digits, ab is the hours, ranging from 00 to 24, and cd is the minutes, ranging from 00 to 59. (0000 and 2400 hours are equivalent, but one minute past midnight is still represented as 0001).

From his unit, Buck Private Kilroy was assigned to K.P. where he reported to duty on the hour. After a quick, but complete, demonstration on how to peel a potato by the mess sergeant, Kilroy was ordered to peel two potatoes every minute from abcd hours until efgh hours.

Upon timely completion of the task, the buck private was put to work in other kitchen duties for the remainder of the detail (where he could contemplate the meaning of "hurry up and wait") while waiting for the other members of his company to be called to chow hall at (hgfe + abcd) hours.

The following is known:
(a) The times, abcd, efgh, and (hgfe + abcd), are prime numbers;
(b) Each two digit hour and minute of efgh and (hgfe + abcd) are also prime numbers; and,
(c) The sum of the digits of abcd is divisible by three.
(d) Normal addition rules apply in adding the numbers representing "time" values. If a sum results in a value that is not in the form of a valid time, it obviously does not qualify as a solution.

According to the information given in the problem above, answer the following:
(1) What hour did Kilroy finish peeling potatoes?
(2) Given that the number is prime, how many potatoes were peeled?
(3) And, what time was the company of soldiers called to mess?

 Submitted by Dej Mar Rating: 5.0000 (1 votes) Solution: (Hide) Only one prime number exists such that the sum of its digits is divisible by 3. And 3 is that prime. Therefore, Kilroy commenced peeling potatoes at 0003 hours.Only a handful of prime numbers less than 2359 meet the requirement that first and second pairs of digits represent prime numbers. Of these, only one meets the additional conditions that after reversing the order of the digits and adding 3 the resulting number is also prime as well as the two pairs of digits that make up this number. This number is 0211, and adding 3 to its reversed counterpart, 1120, yields 1123. (1) The task was finished at 0211 hours.(2) 257 potatoes. Kilroy had peeled 256 potatoes + 1 potato peeled by the mess sergeant. (3) Mess was called at 1123 hours.

 Subject Author Date re(2): Solution tomarken 2006-06-01 22:08:36 re: Solution Mindrod 2006-05-31 21:57:33 Solution tomarken 2006-05-31 09:57:30

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