EE.8 Special digital clock

It expresses as A < B that B is larger than A.
There is a relation among the six integers A, B, C, D, E, and F called 0 < A < B < C < D < E < F and A + B + C + D = 15.

(1) How many kinds of combination of (A, B, C, D) is considered in this situation ?

(2) Furthermore, there is additional relation as A + C + E = 21, B + D + F = 42 and D + E + F = 56 to be considered further.

I made a digital clock of 24 hour display of which upper part expresses o’clock with the sum total of ● mark and lower part expresses minutes with the sum total of ● mark.

For example, the table below expressed 15:21.


Then, what time does the next table express?



(3) What does display of the digital clock express 2009 minutes after the time when it was found by (2)?
Write in the following digital clock.





Answer
(1) 6 ways
(2) 10:53
(3)