P6 numbers (fr Keith Tan, heuristics: pattern, make-a-list)

A telephone number consists of 10 digits. If the third number must start with either a 9 or 8 and the numbers in the number cannot be used more than thrice, how many possible telephone number combinations can there be if the first two digits in the front of the last 8 numbers must not add up to 10?
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Warning! This is more complicated than meets the eye!

P6 Geometry, clock (algebra, fr CCL)

Solve this extension to the earlier question:

(a) How many occasions are there when the minute hand and the hour hand coincide with each other?
(b) When are these occasions* ?
(c) What are the angles of both the hands clockwise from the position "12" at those instances where both hands coincide?

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* Warning! Except for the first and most trivial case (1200) the other cases comprise weird fractions (with minutes expressed as mixed numbers) :)


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If you have done your due diligence to solve the problem, check your answers against mine:
click here.

P6 geometry, time ("clock geometry" fr CCL)

What is the size of the acute angle between the minute hand and the hour hand for the following cases:
(a) 06 00
(b) 06 30
(c) 12 34
(d) 16 44
(e) 15 33

Give your answers in degrees, if applicable in mixed numbers in in the simplest form.

P5 Ratio (Fr: Xavier Sng)

P5 Average (fr Kanzen )

P5 Whole numbers (fr Kanzen )