05-20-2015, 09:37 AM

05-20-2015, 11:27 AM

(05-20-2015 09:37 AM)Gerald H Wrote: [ -> ]Order of operations argument or find a solution?

http://www.theguardian.com/science/alexs...d-teachers

Quote:multiply first, then division

Let's go with argument first, that's more important than solutions.

05-20-2015, 11:33 AM

Pedantic - me?

Order of operations sort of defined in Guardian text.

Two types of action - quibble or solve.

Order of operations sort of defined in Guardian text.

Two types of action - quibble or solve.

05-20-2015, 12:58 PM

Solvers win - answer found. Quibblers remain confounded.

05-20-2015, 01:24 PM

Let's assume the 10 variables are named A through I, and that we're doing the standard order of operations here (multiplication and division together from left to right, then addition and subtraction together from left to right).

If we assume that non-integer intermediate results are allowable (e.g. G * H / I can be 1 * 4 / 8), then there are 120 valid solutions (verified via brute force with Heap's algorithm in C# - no, I'm not going to generate 362,880 permutations with a 9-level recursive algorithm on my 48*).

If we stipulate that 13 * B / C and G * H / I must have integer results, then there are 20 valid solutions.

*Although, there is a 3-day weekend coming up...

If we assume that non-integer intermediate results are allowable (e.g. G * H / I can be 1 * 4 / 8), then there are 120 valid solutions (verified via brute force with Heap's algorithm in C# - no, I'm not going to generate 362,880 permutations with a 9-level recursive algorithm on my 48*).

If we stipulate that 13 * B / C and G * H / I must have integer results, then there are 20 valid solutions.

*Although, there is a 3-day weekend coming up...

05-20-2015, 01:30 PM

Pedantic - me?

A to I traditionally 9 letters & same number of variables.

A to I traditionally 9 letters & same number of variables.

05-20-2015, 01:35 PM

(05-20-2015 01:30 PM)Gerald H Wrote: [ -> ]Pedantic - me?

A to I traditionally 9 letters & same number of variables.

Er, yeah, 9 variables, not 10. Us CS guys and our off-by-one errors...

05-20-2015, 09:01 PM

I wrote a UserRPL program (HP50G) for this.

With the emulator the first solution is found in few minutes. Non-integer intermediate results are allowed.

Program still running. 22 solutions found for now.

With the emulator the first solution is found in few minutes. Non-integer intermediate results are allowed.

Program still running. 22 solutions found for now.

05-21-2015, 04:04 AM

I've found one solution using paper and pencil only, but I'm not pleased with my work. I assumed all intermediate results are integer. This implies c = 1, because 13 is prime. I didn't figure out any other way than atributing values to three variables (i, b and e) and changing them sequentially as they proved to be impossible. It took no more than an hour and a sheet of paper to find the solution, but that would be too much during an examination though.

No spoiler:

a.b.d.e = 120

f.g.h.i = 3024

No spoiler:

a.b.d.e = 120

f.g.h.i = 3024

05-21-2015, 05:30 AM

(05-21-2015 04:04 AM)Gerson W. Barbosa Wrote: [ -> ]I've found one solution using paper and pencil only, but I'm not pleased with my work. I assumed all intermediate results are integer. This implies c = 1, because 13 is prime. I didn't figure out any other way than atributing values to three variables (i, b and e) and changing them sequentially as they proved to be impossible. It took no more than an hour and a sheet of paper to find the solution, but that would be too much during an examination though.

No spoiler:

a.b.d.e = 120

f.g.h.i = 3024

Factors check out as a possibly good solution.

05-21-2015, 08:12 AM

Since I'm in Haskell at the moment, I gave it a go, it is quite a simple exercise.

For what it matters, I found 128 solutions instantly... wow.

Haskell code

Solutions

For what it matters, I found 128 solutions instantly... wow.

Haskell code

Code:

`import Data.List`

[x | x <- permutations [1..9], (x!!0+13*x!!1/x!!2+x!!3+12*x!!4-x!!5-11+x!!6*x!!7/x!!8-10)==66]

Solutions

Code:

126478539

426178539

126478359

426178359

296351478

396251478

132956478

932156478

714965328

914765328

734165928

734165298

134765928

134765298

314279568

214379568

796152438

196752438

912567438

512967438

714965238

914765238

236179458

136279458

314279658

214379658

296351748

236179548

136279548

396251748

132956748

932156748

796152348

196752348

912567348

512967348

948567132

948567312

548967132

548967312

496158732

196458732

764859132

764859312

864759132

864759312

364958172

364958712

964358172

964358712

196458372

496158372

286941753

986241753

286941573

986241573

139478256

139478526

324851976

324851796

132458976

132458796

248179356

148279356

439178256

439178526

824351976

824351796

432158976

432158796

248179536

148279536

941527836

941527386

321547986

321547896

352148976

352148796

152348976

152348796

521347986

521347896

153942876

953142876

153942786

953142786

752849136

752849316

852749136

852749316

852147936

852147396

152847936

152847396

541927836

541927386

328651974

328651794

931625874

931625784

628351974

628351794

631925874

631925784

693521874

693521784

928765134

928765314

728965134

728965314

732859164

732859614

731526984

731526894

832759164

832759614

892315764

392815764

892315674

392815674

872539164

872539614

572839164

572839614

531726984

531726894

593621874

593621784

05-21-2015, 08:41 AM

Do you, Tugdual, claim your list of solutions is exhaustive?

05-21-2015, 10:51 AM

(05-21-2015 08:41 AM)Gerald H Wrote: [ -> ]Do you, Tugdual, claim your list of solutions is exhaustive?Yes I would think so unless my Haskell code is wrong but I checked a few combinations and they look good.

05-21-2015, 11:21 AM

05-21-2015, 11:53 AM

(05-21-2015 11:21 AM)Gerald H Wrote: [ -> ]I think there are 128 in my list and this is what Haskell returned.(05-21-2015 10:51 AM)Tugdual Wrote: [ -> ]Yes I would think so unless my Haskell code is wrong but I checked a few combinations and they look good.

I only see 127 solutions?

Do you expect more?

05-21-2015, 12:02 PM

I beg your pardon, Tugdual, I miscounted.

I only expected one solution & was happy when I found one.

Bravo on your quick research.

I only expected one solution & was happy when I found one.

Bravo on your quick research.

05-21-2015, 12:19 PM

05-21-2015, 12:29 PM

(05-21-2015 12:02 PM)Gerald H Wrote: [ -> ]I beg your pardon, Tugdual, I miscounted.Thanks but no glory, Haskell is quite amazing for that sort of brute force...

I only expected one solution & was happy when I found one.

Bravo on your quick research.

Now I guess the real fun to stick on the forum topic would be to find a clever solution to do that with a simple calculator.

05-21-2015, 01:14 PM

(05-21-2015 12:29 PM)Tugdual Wrote: [ -> ]Thanks but no glory, Haskell is quite amazing for that sort of brute force...

Now I guess the real fun to stick on the forum topic would be to find a clever solution to do that with a simple calculator.

Or maybe somebody brings Haskell to the HP 50g?

Cheers

Thomas

05-21-2015, 01:18 PM

(05-21-2015 11:53 AM)Tugdual Wrote: [ -> ]I think there are 128 in my list and this is what Haskell returned.Yes, I do expect more.

Do you expect more?

Your list is missing 8 additional solutions (due to rounding errors), there are 136 solutions in total - here the missing 8:

183745269

183745629

269851473

269851743

783145269

783145629

869251473

869251743

If you rewrite your equation (avoiding the 2 divisions by multiplying with the 2 denominators), then your program will give you all 136 solutions.

Edit: Or change the test to something like abs(expr-66)<1e-3 ...

Franz