Birthday problem: Difference between revisions

The method used is to find the average number of people to share a common birthday,   and then use the   '''floor'''   of that

<br>that value &nbsp; (less the group size) &nbsp; as a starting point to find a new group size with an expected size that exceeds

<br>50% common&nbsp; duplicate birthdays of the required size.

<lang rexx>/*REXX programpgm examines the birthday problem via random number# simulation. (with specifable parms)*/

parse arg grpsdups samp seed . /*get optional arguments from the CL. */

if grpsdups=='' | grpsdups=='",'" then grpsdups=5 10 /*Not specified? Then use the default.*/

if samp=='' | samp=='",'" then samp=100000 10000 /* " " " " " " */

if datatype(seed, 'W') then call random ,,seed /*RANDOM seed given for repeatability ?*/

diy =365 /*or: diy=365.25 */ /*the number of Days In a Year. */

do g=2 to dups; s=0 /*perform [↓] get a rough estimate forthrough %. 2 ──► duplicate size*/

do g=2 to grps; do s=0 samp; @.=0 /*perform throughsome number of trials. 2 ──► group size. */

do samp; @. do j=0 until @.day==g /*perform someuntil numberG of trialsdup. birthdays found.*/

do j=1 until @.day==g day=random(1, diyM) % 100 /*perform untilexpand Grange dup.RANDOM birthdaysnumber found.generation*/

@.day=random(1,diyM)@.day %+ 1 100 /*expandrecord range RANDOMthe number generationof common birthdays*/

@.day=@.day+1 end /*j*/ /*record [↓] adjust for the number ofDO common birthdaysloop index.*/

end s=s + /*j*/ /*add [↓]number of adjustbirthday forhits theto sum. DO loop index.*/

s=s+j-1 end /*samp*/ /* [↓] % /*add1 number of birthdayrounds hitsdown tothe sumdivision. */

end start.g= s/samp % 1 - g /*sampdefine where the try─outs start. */

say ' end required /*g*/ trial % with required'

say ' do g=2 to dups required group % with required' /*perform through 2 ──► duplicate size*/

say ' do try=start.g until s/samp>=.5; commons=0 /* " size try─outs until average ≥ common birthdays'50%.*/

say ' do samp; ──────── ───── ────────────────' @.=0 /* " some number of trials. */

do try; day=random(1, diyM) % 100 /* [↓] where" the try-outs until happenG dup. birthdays found.*/

do g=2 to grps @.day=@.day + 1 /*performrecord throughthe number 2 ──► group size. of common birthdays*/

do try if @.day==start.g; then do; s=0s+1; leave; end /*found enough G (birthday) hits ? /*perform try-outs until average > 50%.*/

end day/*try=random(1,diyM)start.g*/ % 100 /*expand range[↑] where the try─outs happen. RANDOM number generation*/

end if @.day\==/*g*/ then iterate /*notstick enougha Gfork (birthday)in hitsit, found ?we're all done. */</lang>

sample size is 10000010000

required group trial % with required

common duplicates size common birthdays

2 23 50.709002300%

3 8887 5150.232002400%

4 187 50.151003800%

5 314312 50.778000100%

6 460458 50.006005200%

7 623622 50.648003900%

8 798 50.007001700%

9 985984 50.134005700%

10 11811182 5051.222004000%