perplexus.info :: Numbers : Will take some time ??

Will take some time ?? (Posted on 2018-05-18)

Found on the web:
begin
260723233115686*1931
43744839742282591947
1181326544136*5138222
186378732807587076747
519650114814905002347

Any three of these numbers add up to a perfect square.
end

I have no means to check whether it is a true statement and revised
just 3 possible combinations by adding mod 100 the 2 last digits, i.e. 47+47+47= 41, 47+47+22=96 and 47+47+31=25.
I leave it to the solvers to check the 10 possible combinations and to explain what means were used and what was the runtime.
To make it more interesting 2 distinct digits I've replaced by an asterisk "*".

Have fun finding if the statement is true!
If so - for what values of the asterisks?

See The Solution Submitted by Ady TZIDON

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computer solution

| Comment 1 of 5

About 2 hours to develop and debug the program and 4.726 seconds to run it.

The program is written in UBASIC, which provides more than enough precision to do the arithmetic on numbers of these lengths. The interpreter for that version of Basic is a DOS program so it necessitated running under the DOSBox emulator, as firing up the old XP machine, which ran DOS programs natively, was not worthwhile for shortening the 4.726 second run time (estimate it would have taken about a quarter or a fifth of a second as speed would have been about 20x faster).

The ten square roots appear to the right of each total, which in turn appears under the three summands which comprise it. The first and second *'s are 6 and 7 respectively.

I've done some manual alignment in the output below:

  26072323311568661931
  43744839742282591947
 118132654413675138222
 187949817467526392100   13709479110
 
  26072323311568661931
  43744839742282591947
 186378732807587076747
 256195895861438330625   16006120575
 
  26072323311568661931
  43744839742282591947
 519650114814905002347
 589467277868756256225   24278947215
 
  26072323311568661931
 118132654413675138222
 186378732807587076747
 330583710532830876900   18181961130
 
  26072323311568661931
 118132654413675138222
 519650114814905002347
 663855092540148802500   25765385550
 
  26072323311568661931
 186378732807587076747
 519650114814905002347
 732101170934060741025   27057368145
 
  43744839742282591947
 118132654413675138222
 186378732807587076747
 348256226963544806916   18661624446
 
  43744839742282591947
 118132654413675138222
 519650114814905002347
 681527608970862732516   26106083754
 
  43744839742282591947
 186378732807587076747
 519650114814905002347
 749773687364774671041   27381995679
 
 118132654413675138222
 186378732807587076747
 519650114814905002347
 824161502036167217316   28708213146

4.726

5 clr time

10 kill "wtsomtim.txt":open "wtsomtim.txt" for output as #1

40 dim S$(5),S0$(5)

60 S0$(1)="260723233115686*1931"

70 S0$(2)="43744839742282591947"

80 S0$(3)="1181326544136*5138222"

90 S0$(4)="186378732807587076747"

100 S0$(5)="519650114814905002347"

110

120 for A=0 to 9

130 for B=0 to 9

140 for I=1 to 5

150 S$(I)=S0$(I)

160 next

170 Ix1=instr(S$(1),"*")

180 mid(S$(1),Ix1,1)=cutspc(str(A))

190 Ix1=instr(S$(3),"*")

200 mid(S$(3),Ix1,1)=cutspc(str(B))

210

220 Good=1

230 for I=1 to 3

240 for J=I+1 to 4

250 for K=J+1 to 5

260 Tot=val(S$(I))+val(S$(J))+val(S$(K))

270 Sr=int(sqrt(Tot)+0.5)

280 if Sr*Sr<>Tot then Good=0

290 next

300 next

310 next

320

330 if Good then

340 :for I=1 to 3

350 :for J=I+1 to 4

360 :for K=J+1 to 5

370 :Tot=val(S$(I))+val(S$(J))+val(S$(K))

380 :Sr=int(sqrt(Tot)+0.5)

390 :print #1,S$(I)

400 :print #1,S$(J)

410 :print #1,S$(K)

420 :print #1,Tot,Sr

430 :next

440 :next

450 :next

455 :print #1,

470

480 next B

490 next A

500 print #1,time1000/1000

510 close #1

Posted by Charlie on 2018-05-18 13:41:56

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