Puzzles with numbers and things

[snookersfun]

so how many did you get Sarmu? (after the first count?). It is not supposed to be a puzzle....

[Sarmu]

so how many did you get Sarmu? (after the first count?). It is not supposed to be a puzzle....

6.........................

[snookersfun]

highly intelligent!So, now you can go on to the other puzzles

[snookersfun]

round 113: total clearance

Apparently Mark Selby had a total clearance of 120 to win his match this morning.

This had me thinking how many possible colour combinations are there to achieve a total clearance of 120?
(e.g.: 6 colours, 15 reds + 9 blacks, 1 blue, 5 yellows)

Please put up your answers on the thread.

[davis_greatest]

OK - so in this question, order is not important, right?

E.g.

14 reds with blacks, followed by red-pink (and the colours)

would be the same as

red-pink, followed by 14 reds with blacks (and the colours)

[snookersfun]

yes, let's go for that one first.
anybody welcome to calculate the other option as well though (for huge fame)...

[davis_greatest]

Looks like quite a big number. I have my answer - want to hear it? I can't immediately see a simple way of solving this (other than using an iterative formula) (or, of course, counting them out by hand - but I'd never do that )...

[snookersfun]

so, what do you have? Let's hear it.
Hope it is anywhere close to my scribble...

[davis_greatest]

OK, I've PM'ed you the answer...

[davis_greatest]

OK, here is the number of ways of making each possible total clearance, for every break except 120

Break... Ways

72 …. 1
73 …. 1
74 …. 2
75 …. 3
76 …. 5
77 …. 7
78 …. 10
79 …. 13
80 …. 18
81 …. 23
82 …. 30
83 …. 37
84 …. 47
85 …. 57
86 …. 70
87 …. 84
88 …. 100
89 …. 117
90 …. 137
91 …. 157
92 …. 180
93 …. 203
94 …. 228
95 …. 253
96 …. 280
97 …. 306
98 …. 333
99 …. 359
100 …. 385
101 …. 409
102 …. 433
103 …. 453
104 …. 472
105 …. 488
106 …. 501
107 …. 511
108 …. 518
109 …. 521
110 …. 521
111 …. 518
112 …. 511
113 …. 501
114 …. 488
115 …. 472
116 …. 453
117 …. 433
118 …. 409
119 …. 385
120 ….
121 …. 333
122 …. 306
123 …. 280
124 …. 253
125 …. 228
126 …. 203
127 …. 180
128 …. 157
129 …. 137
130 …. 117
131 …. 100
132 …. 84
133 …. 70
134 …. 57
135 …. 47
136 …. 37
137 …. 30
138 …. 23
139 …. 18
140 …. 13
141 …. 10
142 …. 7
143 …. 5
144 …. 3
145 …. 2
146 …. 1
147 …. 1

[snookersfun]

very impressive! not too close to my scribbles, but that is due to just that (what was I thinking...)

That means it is probably high time to close rounds 110-113. d_g has solved them all and will hopefully put up his solutions and explanations later on. Abextra had solved round 110! Well done

[dantuck_7]

ROUND 114

Carrying on from the number of ways of making each of the total clearances above. Could someone post all the possible ways of making a break of 1 through to a break of 147.

But the order would be important so - green,yellow - is different from yellow,green.

Thanks Dan.

[davis_greatest]

ROUND 114

Carrying on from the number of ways of making each of the total clearances above. Could someone post all the possible ways of making a break of 1 through to a break of 147.

But the order would be important so - green,yellow - is different from yellow,green.

Thanks Dan.

That sounds a lot of work hehe. Do you mean post the number of ways of making each break, rather than listing every possible break (which would be a very very long list)?

I'll post later (when I get a few minutes) the number of ways of making every possible total clearance where the order matters - that's not too hard ... to work out however all breaks other than total clearances would need a lot more effort.

[davis_greatest]

very impressive! not too close to my scribbles, but that is due to just that (what was I thinking...)

That means it is probably high time to close rounds 110-113. d_g has solved them all and will hopefully put up his solutions and explanations later on. Abextra had solved round 110! Well done

OK - I'll look back over them now and see if I remember my answers...

[davis_greatest]

one more on special request

A young boy, his father and his mother were celebrating a birthday.
This got the young boy to thinking about their ages. Upon asking
his father about this, the father told him: "Well, right now I am
six times your age, and all together the sum of our ages (yours,
mine, and your mother's) is 70. Later on, when I am only twice
your age, that sum will be twice what it is now."

Who's birthday is it?

I've forgotten all my answers so am having to work them out again. The answer to this one is that it is Daddy's birthday - he was 35.

Mummy was 29 year and 2 months and little boy was 5 years and 10 months.