# mobile date puzzle

A mobile company launched six mobile models — S,P,O, K, M and Z in the span of eight years. No two models were launched within a period of 18 months. The launch dates of the models are given below:

S      31st January
P      20th February
O      1st April
K      19th June
M      20th September
Z      5th November


find the exact date on which they were launched.

Source : Me

Here's the solution (I'm using the years 01 - 09 for simplicity):

P 20/02/01
M 20/09/02
O 1/4/04
Z 5/11/05
K 19/06/07
S 31/01/09

Dates range from 20/02/01 to 31/01/09, just less than 8 years.

Here's my approach:

I took two dates which were just outside 6 months apart, 01/04 and 05/11. Incidentally, these and [20/02, 20/09] give the same overall result.

Then I looked for a date in September (19 months before April) and a date in June (19 months after November). So my list looked like [20/09, 01/04, 05/11, 19/06].

Once I had those filled in I only had to fit in February and January. I knew that if I put January in first then the total time would be >8 yrs, so February had to go at the beginning and January had to go at the end, giving the final list [20/02, 20/09, 01/04, 05/11, 19/06, 31/01].

Once I had all six dates in, I checked that they all fit in the 8-year period and were all at least 18 months apart, and pressed solve!

• Can you pls tell the approach? – sam Oct 30 '18 at 12:36
• Added it in an edit. – Joseph Mulligan Oct 30 '18 at 13:09