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ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 97
  • Posts: 4628
Thanks for this post from:
charliepatrick
February 25th, 2021 at 11:20:03 AM permalink
Quote: Wizard

Looks like Charlie is winning the WoV golf match so far and I'm losing, which is usually the case when I golf.


I did a brute force search on every pair of driver and approach clubs in 25-yard intervals up to 500 yards, and get the same answer Charlie got.



Note that X indicates that reaching that hole is impossible
LongShort123456789Score
502536576759957
752524455636742
755024454536639
1002533444536537
10050233XX4X5XX
1007523343435532
1252524253436534
1255033244435432
1257524233434530
12510033234324428
1502512433443428
15050123XX3X3XX
1507512XXXX23XX
150100122XX3X3XX
15012512242673330
1752524435236534
1755033443224530
1757524233234326
17510043352263432
17512562275236336
17515012729253839
2002535354424333
20050232XX3X3XX
2007524432335430
200100X2XXXXXXXX
20012548223563740
200150123XX2X3XX
2001751295117236459
2252544253612330
2255035532412530
2257522XXXX12XX
22510053427312330
225125106239212540
22515012XXXX12XX
2251756121053212950
2252001273951112252
2502553142524531
25050321XX3X3XX
2507524125436330
250100231XX2X3XX
250125XX1XXXXXXX
250150121XX3X3XX
2501754813132612251
250200631XX5X2XX
2502251251739121555
2752562231436734
2755036521624433
2757524651236332
27510063581493746
2751252427110116346
275150124121973241
275175126141112921370
27520048131513612567
27522561210311412756
275250123151718151375
3002561322347634
30050312XX2X4XX
3007521XXXX23XX
300100X1XXXXXXXX
3001259121184510252
30015011XXXXX2XX
300175101491221511367
300200X1XXXXXXXX
30022541XXXX12XX
300250611XX3X7XX
3002751212031518131184
3252562413256534
3255036512736336
3257524217636536
325100736110524240
3251256122158921156
32515012111144831357
3251752410172136954
3252001594117141231186
325225146161111812372
325250481115176121983
3252756121011142118588
3253001212012231811997
3502563524165436
35050323XX1X3XX
3507524872136235
350100332XX1X2XX
3501251492513124858
350150125XX1X3XX
350175XXXXX1XXXX
350200247XX1X6XX
35022571441991121673
350250961XX1X3XX
35027548151711612367
3503006110XX1X5XX
35032512242012211897114
3752564635274340
3755036523748240
3757522XXXX32XX
37510083711261251064
375125XX2XXXXXXX
37515012XXXX23XX
3751751814817112510792
375200510167134191518107
37522524XXXX12XX
375250XX1XXXXXXX
3752751661813120112215122
37530041XXXX63XX
375325612101251423183112
375350122420262211875135
4002565746383244
40050334XX2X2XX
4007524329836744
400100X2XXXXXXXX
40012536210214159566
400150122XX5X3XX
40017591815852241477
400200XXXXXXXXXX
4002251671018214121291
400250241XX9X6XX
400275242141611191823127
400300X1XXXXXXXX
40032548261171961221114
40035061210XX1X3XX
4003751224202622281853158
4252566857492148
4255036534759143
42575241093236140
425100938213736152
425125122215116714170
42515012617213103155
42517561225192918174
425200181151481724180
4252258162213191012192
425250211512374189199
42527524229114176176
425300141411162321131104
425325186201132227241132
425350481719281612196
4253756121029271425181142
4254001224202622281831154
4502567968591253
45050345XX3X1XX
4507523XXXX31XX
450100433XX2X1XX
450125816227111211574
45015012XXXXX1XX
4501751792016221311999
450200952XX8X1XX
450225XXXXXX11XX
4502505101XX7X1XX
450275102071214151979
45030021XXXXX1XX
450325211141231816113108
45035011613XX1X1XX
45037548XXXX61XX
45040061210XX14X1XX
4504251224202622281811152
47525681079692360
4755036545769247
475752443111036952
475100103914381571382
475125181227172361178
475150121521961131877
4751751426131722116596
4752006121922259188101
475225188211514122384
47525011221192516247107
4752752418107126211223142
475300151251712471427122
475325241419261961192
475350918425111302720145
47537520622153124132617174
475400483032192161223155
4754256121031291427181148
47545012242026222818134185
500256910810793466
50050355XX4X2XX
500752412114336247
500100X3XXXXXXXX
500125XX2XXXXXXX
500150127XX2X3XX
500175361421021891377
500200X2XXXXXXXX
500225918155221121184
500250XX1XXXXXXX
500275221316271102421116
500300X1XXXXXXXX
5003253027171224122419156
500350249XX1X6XX
500375XX4XXXXXXX
500400X6XXXXXXXX
50042548192132346121137
50045061210XX14X1XX
500475122420262228183634220


Last edited by: ThatDonGuy on Feb 25, 2021
charliepatrick
charliepatrick
Joined: Jun 17, 2011
  • Threads: 33
  • Posts: 2322
February 25th, 2021 at 11:38:05 AM permalink
Thanks - the guess was only based on an observation...
the logic that you needed a long club to get near the higher numbers and with 7/3 I could see you could easily get 10, 14 and 17.
Gialmere
Gialmere
Joined: Nov 26, 2018
  • Threads: 39
  • Posts: 1821
February 25th, 2021 at 5:20:56 PM permalink
Quote: charliepatrick

I'll have to think about an analytical approach to this but I did like my first guess....

Dividing all the lengths by 25 gets 6 12 10 13 11 14 9 17 18 = 6 17 18 (9 thru 14). 7 and 3 (i.e. 175 and 75 yards) gives 26 shots. (2 4 2 3 3 2 3 3 4).


Correct!!


Quote: ThatDonGuy

I did a brute force search on every pair of driver and approach clubs in 25-yard intervals up to 500 yards, and get the same answer Charlie got.



Note that X indicates that reaching that hole is impossible
LongShort123456789Score
502536576759957
752524455636742
755024454536639
1002533444536537
10050233XX4X5XX
1007523343435532
1252524253436534
1255033244435432
1257524233434530
12510033234324428
1502512433443428
15050123XX3X3XX
1507512XXXX23XX
150100122XX3X3XX
15012512242673330
1752524435236534
1755033443224530
1757524233234326
17510043352263432
17512562275236336
17515012729253839
2002535354424333
20050232XX3X3XX
2007524432335430
200100X2XXXXXXXX
20012548223563740
200150123XX2X3XX
2001751295117236459
2252544253612330
2255035532412530
2257522XXXX12XX
22510053427312330
225125106239212540
22515012XXXX12XX
2251756121053212950
2252001273951112252
2502553142524531
25050321XX3X3XX
2507524125436330
250100231XX2X3XX
250125XX1XXXXXXX
250150121XX3X3XX
2501754813132612251
250200631XX5X2XX
2502251251739121555
2752562231436734
2755036521624433
2757524651236332
27510063581493746
2751252427110116346
275150124121973241
275175126141112921370
27520048131513612567
27522561210311412756
275250123151718151375
3002561322347634
30050312XX2X4XX
3007521XXXX23XX
300100X1XXXXXXXX
3001259121184510252
30015011XXXXX2XX
300175101491221511367
300200X1XXXXXXXX
30022541XXXX12XX
300250611XX3X7XX
3002751212031518131184
3252562413256534
3255036512736336
3257524217636536
325100736110524240
3251256122158921156
32515012111144831357
3251752410172136954
3252001594117141231186
325225146161111812372
325250481115176121983
3252756121011142118588
3253001212012231811997
3502563524165436
35050323XX1X3XX
3507524872136235
350100332XX1X2XX
3501251492513124858
350150125XX1X3XX
350175XXXXX1XXXX
350200247XX1X6XX
35022571441991121673
350250961XX1X3XX
35027548151711612367
3503006110XX1X5XX
35032512242012211897114
3752564635274340
3755036523748240
3757522XXXX32XX
37510083711261251064
375125XX2XXXXXXX
37515012XXXX23XX
3751751814817112510792
375200510167134191518107
37522524XXXX12XX
375250XX1XXXXXXX
3752751661813120112215122
37530041XXXX63XX
375325612101251423183112
375350122420262211875135
4002565746383244
40050334XX2X2XX
4007524329836744
400100X2XXXXXXXX
40012536210214159566
400150122XX5X3XX
40017591815852241477
400200XXXXXXXXXX
4002251671018214121291
400250241XX9X6XX
400275242141611191823127
400300X1XXXXXXXX
40032548261171961221114
40035061210XX1X3XX
4003751224202622281853158
4252566857492148
4255036534759143
42575241093236140
425100938213736152
425125122215116714170
42515012617213103155
42517561225192918174
425200181151481724180
4252258162213191012192
425250211512374189199
42527524229114176176
425300141411162321131104
425325186201132227241132
425350481719281612196
4253756121029271425181142
4254001224202622281831154
4502567968591253
45050345XX3X1XX
4507523XXXX31XX
450100433XX2X1XX
450125816227111211574
45015012XXXXX1XX
4501751792016221311999
450200952XX8X1XX
450225XXXXXX11XX
4502505101XX7X1XX
450275102071214151979
45030021XXXXX1XX
450325211141231816113108
45035011613XX1X1XX
45037548XXXX61XX
45040061210XX14X1XX
4504251224202622281811152
47525681079692360
4755036545769247
475752443111036952
475100103914381571382
475125181227172361178
475150121521961131877
4751751426131722116596
4752006121922259188101
475225188211514122384
47525011221192516247107
4752752418107126211223142
475300151251712471427122
475325241419261961192
475350918425111302720145
47537520622153124132617174
475400483032192161223155
4754256121031291427181148
47545012242026222818134185
500256910810793466
50050355XX4X2XX
500752412114336247
500100X3XXXXXXXX
500125XX2XXXXXXX
500150127XX2X3XX
500175361421021891377
500200X2XXXXXXXX
500225918155221121184
500250XX1XXXXXXX
500275221316271102421116
500300X1XXXXXXXX
5003253027171224122419156
500350249XX1X6XX
500375XX4XXXXXXX
500400X6XXXXXXXX
50042548192132346121137
50045061210XX14X1XX
500475122420262228183634220



If you're looking for another round of golf...

According to the programming website I found this puzzle at, in addition to the set {175, 75}, there is another set of numbers that will complete the course in the minimum of 26 strokes. They don't post the answer but, from ThatDonGuy's list, they're not a multiples of 25 (and possibly not even whole numbers).

--------------------------------

Have you tried 22 tonight? I said 22.
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 97
  • Posts: 4628
February 25th, 2021 at 6:23:01 PM permalink
Quote: Gialmere

If you're looking for another round of golf...

According to the programming website I found this puzzle at, in addition to the set {175, 75}, there is another set of numbers that will complete the course in the minimum of 26 strokes. They don't post the answer but, from ThatDonGuy's list, they're not a multiples of 25 (and possibly not even whole numbers).


I have checked every combination of clubs that are multiples of 0.1 yards up to 900, but can't find any other than the one posted solution.
Gialmere
Gialmere
Joined: Nov 26, 2018
  • Threads: 39
  • Posts: 1821
February 25th, 2021 at 8:32:56 PM permalink
Quote: ThatDonGuy

Quote: Gialmere

If you're looking for another round of golf...

According to the programming website I found this puzzle at, in addition to the set {175, 75}, there is another set of numbers that will complete the course in the minimum of 26 strokes. They don't post the answer but, from ThatDonGuy's list, they're not a multiples of 25 (and possibly not even whole numbers).


I have checked every combination of clubs that are multiples of 0.1 yards up to 900, but can't find any other than the one posted solution.


Oops! My bad. I messed up one of the hole lengths. Hole #8 is only 400 yds. Fortunately the 75/175 solve works for either length but, apologies to ThatDonGuy.

The correct length does, however, make the second solve much simpler.
Have you tried 22 tonight? I said 22.
charliepatrick
charliepatrick
Joined: Jun 17, 2011
  • Threads: 33
  • Posts: 2322
February 25th, 2021 at 9:45:38 PM permalink
Quote: Gialmere

...
Oops! My bad. I messed up one of the hole lengths. Hole #8 is only 400 yds. Fortunately the 75/175 solve works for either length but, apologies to ThatDonGuy....

Yes 150 125 works (1 2 2 4 2 5 4 3 3). 200/75 and 250/75 now get close with 27 shots.
btw I couldn't see how fractional ones could easily work as to get to 26 strokes you need at least one hole which is a 2. So if the clubs were X+fraction and Y-fraction (fraction=1/2 1/3 etc) then the only way to get whole numbers is X-Y 2X-2Y nX etc. Apart from 6 and 12 you have no others that are double.
Also you know that some combinations can't work, such as when both clubs are a multiple of 50 or where one club is a multiple of the other. However if using a brute force method that's not worth worrying about.
teliot
teliot
Joined: Oct 19, 2009
  • Threads: 39
  • Posts: 2159
February 25th, 2021 at 10:10:00 PM permalink
This very nice problem about golfing is also related to the postage stamp problem and minimizing total stamp usage across a variety of postages. Well, maybe not that related since you can't have negative stamps.

Postage Stamp Problem
Given stamps with postage x and y, relatively prime, you can always make every postage above (x - 1) * (y - 1).

I believe finding a closed form solution for the postage stamp problem for three postages is still unsolved.
Personal website: www.ijmp.org
ThatDonGuy
ThatDonGuy
Joined: Jun 22, 2011
  • Threads: 97
  • Posts: 4628
February 26th, 2021 at 7:15:42 AM permalink
Quote: Gialmere

Oops! My bad. I messed up one of the hole lengths. Hole #8 is only 400 yds. Fortunately the 75/175 solve works for either length but, apologies to ThatDonGuy.

The correct length does, however, make the second solve much simpler.


I checked every possible pair of different clubs that are multiples of 1/5, 1/6, 1/7, and 1/8 yard up to 1000 yards, and still get 175/75 as the only 26-stroke solution.

Update: now up through 1/14 of a yard - still only one solution for 26 (and two for 27).
Last edited by: ThatDonGuy on Feb 26, 2021
gordonm888
gordonm888
Joined: Feb 18, 2015
  • Threads: 44
  • Posts: 2809
February 26th, 2021 at 6:18:21 PM permalink



EDIT:
If the 8th hole is only 400 yds, rather than 450:

250 and 75 seems to yield just 27 strokes

150 =75+75_____2
300=75 +75+ 75+75__4
250 = 250 ________1
325 = 250 + 75______2
275 = 250 -75 -75 -75 +250_________5
350 = 250 -75 -75 +250_______4
225 = 75 +75 +75 _______3
400 = 250 +75 +75 _________________3
425 = 250 -75 +250 ____3



EDit: I see that ThatDonGuy has already overwhelmed the problem.
Last edited by: gordonm888 on Feb 26, 2021
So many better men, a few of them friends, are dead. And a thousand thousand slimy things live on, and so do I.
teliot
teliot
Joined: Oct 19, 2009
  • Threads: 39
  • Posts: 2159
February 26th, 2021 at 7:02:26 PM permalink
On the topic of Golfing, let me create a different problem that is based on efficient stamp totals.

Suppose the Post Office issues two values of stamps X cents and Y cents. What are the most efficient values for these two stamps X & Y so that we can make each postage from $1.20 to $2.00, using the least number of stamps overall?

Yeah, "Easy" Math Puzzles. :)
Personal website: www.ijmp.org

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