Products of numbers in 5/39 combos (Fantasy Five)Prev TopicNext Topic

• cottoneyedjoe

  

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  Jan 20, 2021, 10:58 pm

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  I was looking at products of the numbers in CA Fantasy Five combinations. (For example, the combo 2-3-11-13-25 has a product of 21450.) This is probably of interest only to me and a few of AllenB's crickets. I present Five Fun Facts about Fantasy Five Products:

  (1) Although there are 575757 different combinations in a 5/39 game, there are only 55183 distinct products of the five numbers.

  (2) The minimum product is 120 (only achieved with the combination 1-2-3-4-5) and the maximum product is 69090840 (only achieved with the combination 35-36-37-38-39). This one is probably obvious.

  (3) The most common product is 120960, which can be achieved with 290 different combinations.

  (4) 4944 combinations have a product that is a square number.

  (5) Distribution of products:

  • 1/3 of the combos (191917 to be exact) have a product between 120 and 440448.
  • 1/3 of the combos (191911 to be exact) have a product between 440496 and 2245122.
  • 1/3 of the combos (191929 to be exact) have a product between 2245320 and 69090840.
• db101

  

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  Jan 22, 2021, 2:05 pm

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  Wrapping my head around it...looks interesting. How many of those products can only be made one way?
• cottoneyedjoe

  

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  Jan 22, 2021, 3:59 pm

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  In response to db101

  Quote: Originally posted by db101 on Jan 22, 2021

  Wrapping my head around it...looks interesting. How many of those products can only be made one way?

  13916 of them. About 25.2%.
• AllenB

  

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  Jan 22, 2021, 4:38 pm

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  In response to cottoneyedjoe

  Quote: Originally posted by cottoneyedjoe on Jan 20, 2021

  I was looking at products of the numbers in CA Fantasy Five combinations. (For example, the combo 2-3-11-13-25 has a product of 21450.) This is probably of interest only to me and a few of AllenB's crickets. I present Five Fun Facts about Fantasy Five Products:

  (1) Although there are 575757 different combinations in a 5/39 game, there are only 55183 distinct products of the five numbers.

  (2) The minimum product is 120 (only achieved with the combination 1-2-3-4-5) and the maximum product is 69090840 (only achieved with the combination 35-36-37-38-39). This one is probably obvious.

  (3) The most common product is 120960, which can be achieved with 290 different combinations.

  (4) 4944 combinations have a product that is a square number.

  (5) Distribution of products:

  • 1/3 of the combos (191917 to be exact) have a product between 120 and 440448.
  • 1/3 of the combos (191911 to be exact) have a product between 440496 and 2245122.
  • 1/3 of the combos (191929 to be exact) have a product between 2245320 and 69090840.

  All of a sudden there is a lot of chirping coming from the break room. 

  Some of the boys want to see a historical graph showing the Product divided by 55 (groups of 1000). 

  The surfing dude is always looking for waves.
• AllenB

  

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  Jan 22, 2021, 4:49 pm

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  In response to AllenB

  Quote: Originally posted by AllenB on Jan 22, 2021

  All of a sudden there is a lot of chirping coming from the break room. 

  Some of the boys want to see a historical graph showing the Product divided by 55 (groups of 1000). 

  The surfing dude is always looking for waves.

  Dang it Joe.

  I had the crew working on a Pick 3 Tool and now they are mumbling about putting the big Lexi File on and getting all of the products. 

  Some are already guessing that there will be a Lexi Number connection and maybe a pattern with the 5th Perfection Score.

  I'm calling the shop union rep.  These guys work for me, Right?
• cottoneyedjoe

  

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  Jan 22, 2021, 6:17 pm

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  In response to AllenB

  Quote: Originally posted by AllenB on Jan 22, 2021

  All of a sudden there is a lot of chirping coming from the break room. 

  Some of the boys want to see a historical graph showing the Product divided by 55 (groups of 1000). 

  The surfing dude is always looking for waves.

  You showed up in the nick of time. My lizard has been eyeing those crickets. Fantasy Five has had some sweet double rollovers this month, but on days when I wasn't out and about to get tickets. 

  If you want a text file with all the F5 products and their respective counts, let me know and I will see how to link it somewhere for you to download.
• AllenB

  

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  Jan 23, 2021, 1:23 pm

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  In response to cottoneyedjoe

  Quote: Originally posted by cottoneyedjoe on Jan 22, 2021

  You showed up in the nick of time. My lizard has been eyeing those crickets. Fantasy Five has had some sweet double rollovers this month, but on days when I wasn't out and about to get tickets. 

  If you want a text file with all the F5 products and their respective counts, let me know and I will see how to link it somewhere for you to download.

  I appreciate the offer, but, I already have a File that can produce the products and sort the combinations.

  I got the boys back on the current project so it's on the round tuit shelf right now.

  Have you tracked any thing or is this new to you?
• Mr-B 216

  

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  Jan 23, 2021, 6:06 pm

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  Thanks for bringing this up Joe. Here are the top 36 products for OH 5/39 game. Looks like in hindsight, I only needed to play product 523600's 34 combos each day to achieve a jackpot, (or 4) since 2004.

  

  What goes around comes around.
• cottoneyedjoe

  

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  Jan 24, 2021, 12:51 am

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  The 5-number product analysis a bit unwieldy for me due to their being ~55,000 of them, so I've also looked at sums of pair-wise products (SPWPs). There are only 11,098 distinct SPWPs, a slight improvement. Of all the 5/39 combinations it turns out that

  • roughly 1/3 have a SPWP between 85 and 2910
  • roughly 1/3 have a SPWP between 2911 and 4603
  • roughly 1/3 have a SPWP between 4604 and 13685

  Maybe there's another way of looking at products that results in a more manageable set.
• db101

  

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  Jan 25, 2021, 2:11 pm

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  In response to cottoneyedjoe

  Quote: Originally posted by cottoneyedjoe on Jan 22, 2021

  13916 of them. About 25.2%.

  I'm curious about the fact that the number of unique products is about 1/10 of the number of combinations. Is that true for any 5/N game?
• Mr-B 216

  

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  In response to db101

  Quote: Originally posted by db101 on Jan 25, 2021

  I'm curious about the fact that the number of unique products is about 1/10 of the number of combinations. Is that true for any 5/N game?

  Game = 5/n game
  N Combos = 5 number combos available
  P Combos = product combos available
  P/N = percentage of P Combos to N Combos
  One Way = number of products that are only possible using one 5 number combo
  Way/P = percentage of One Way Combos to P Combos

   

  Game	N Combos	P Combos	P/N	One Way	Way/ P Combos
  5/30	142506	17232	12.09%	4526	26.27%
  5/31	169911	23217	13.66%	6551	28.22%
  5/32	201376	25097	12.46%	6728	26.81%
  5/33	237336	27623	11.64%	7226	26.16%
  5/34	278256	30877	11.10%	7943	25.72%
  5/35	324632	33893	10.44%	8513	25.12%
  5/36	376992	35208	9.34%	8596	24.41%
  5/37	435897	45993	10.55%	12005	26.10%
  5/38	501942	50811	10.12%	13031	25.65%
  5/39	575757	55183	9.58%	13916	25.22%
  5/40	658008	57397	8.72%	14147	24.65%
  5/41	749398	73385	9.79%	19198	26.16%
  5/42	850668	76323	8.97%	19294	25.28%
  5/43	962598	96412	10.02%	25831	26.79%
  5/44	1086008	101527	9.35%	26283	25.89%
  5/45	1221759	106528	8.72%	27114	25.45%

  What goes around comes around.
• db101

  

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  Jan 26, 2021, 8:01 pm

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  In response to Mr-B 216

  Quote: Originally posted by Mr-B 216 on Jan 26, 2021

  Game = 5/n game
  N Combos = 5 number combos available
  P Combos = product combos available
  P/N = percentage of P Combos to N Combos
  One Way = number of products that are only possible using one 5 number combo
  Way/P = percentage of One Way Combos to P Combos

   

  Game	N Combos	P Combos	P/N	One Way	Way/ P Combos
  5/30	142506	17232	12.09%	4526	26.27%
  5/31	169911	23217	13.66%	6551	28.22%
  5/32	201376	25097	12.46%	6728	26.81%
  5/33	237336	27623	11.64%	7226	26.16%
  5/34	278256	30877	11.10%	7943	25.72%
  5/35	324632	33893	10.44%	8513	25.12%
  5/36	376992	35208	9.34%	8596	24.41%
  5/37	435897	45993	10.55%	12005	26.10%
  5/38	501942	50811	10.12%	13031	25.65%
  5/39	575757	55183	9.58%	13916	25.22%
  5/40	658008	57397	8.72%	14147	24.65%
  5/41	749398	73385	9.79%	19198	26.16%
  5/42	850668	76323	8.97%	19294	25.28%
  5/43	962598	96412	10.02%	25831	26.79%
  5/44	1086008	101527	9.35%	26283	25.89%
  5/45	1221759	106528	8.72%	27114	25.45%

  Sweet chart Mr-B. Thanks for posting that.
• cottoneyedjoe

  

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  Jan 28, 2021, 10:37 pm

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  In response to Mr-B 216

  Quote: Originally posted by Mr-B 216 on Jan 26, 2021

  Game = 5/n game
  N Combos = 5 number combos available
  P Combos = product combos available
  P/N = percentage of P Combos to N Combos
  One Way = number of products that are only possible using one 5 number combo
  Way/P = percentage of One Way Combos to P Combos

   

  Game	N Combos	P Combos	P/N	One Way	Way/ P Combos
  5/30	142506	17232	12.09%	4526	26.27%
  5/31	169911	23217	13.66%	6551	28.22%
  5/32	201376	25097	12.46%	6728	26.81%
  5/33	237336	27623	11.64%	7226	26.16%
  5/34	278256	30877	11.10%	7943	25.72%
  5/35	324632	33893	10.44%	8513	25.12%
  5/36	376992	35208	9.34%	8596	24.41%
  5/37	435897	45993	10.55%	12005	26.10%
  5/38	501942	50811	10.12%	13031	25.65%
  5/39	575757	55183	9.58%	13916	25.22%
  5/40	658008	57397	8.72%	14147	24.65%
  5/41	749398	73385	9.79%	19198	26.16%
  5/42	850668	76323	8.97%	19294	25.28%
  5/43	962598	96412	10.02%	25831	26.79%
  5/44	1086008	101527	9.35%	26283	25.89%
  5/45	1221759	106528	8.72%	27114	25.45%

  That's really neat. It makes sense that the ratio generally tends to decrease as N increases since the density of primes decreases, and that it has little spikes when N hits a prime.