The New Sudoku Players' Forum

[JPF]

JPF, in case you're really using a program, it'd be good fun to discuss about it too.
...
Do you have a comprehensive list? And how could you be sure?

How did you guess ?

I haven’t quite finished my homework yet.
I need a bit more time to post something safe.

I’ll PM you some first thoughts on the subject.

JPF

PS: what can I get with 1500 points ?

[emm]

The big roller would seem to refute this article

[udosuk]

what can I get with 1500 points ?

My advice would be to make up your own riddle threads and award those points to others... Sharing makes the world a nicer place...

And thanks for the great article emm... I like to program and often make spelling mistakes... But sometimes I'd point out typos by others too... So I don't know what group I belong to...

And BTW seeing underquark has fixed the typo... I decide to not only give him back the missing point but also double his score for being the first to solve the original question... So he's on 100 now (still some distance behind the big roller)...

Here is the grand prize: 10000 points for showing a full list of all combinations with unique formulas, with a solid proof/program as evidence...

[Cec]

The big roller would seem to refute this article :

I couldn't help having a bit of a chuckle when reading emm's above article written by Chris Tomlinson concerning computer programmers' spelling.. It was the second line of the article which made me chuckle but then again, even the spelling checker can't expect to be always perfect.

Cec

[udosuk]

I'm pretty sure there is a list of all solutions out there somewhere anyway.

Here is one I made with my program... I found 466 possible cases (out of 715 total combinations of 4 numbers from 0 to 9)... It'd be very appreciated if someone else could verify this figure with another program...

0038: (0+0)+(3*8)
0046: (0+0)+(4*6)
0128: ((0+1)+2)*8
0136: ((0+1)+3)*6
0137: ((0+1)+7)*3
0138: (0+1)*(3*8)
0139: (9-(0+1))*3
0145: ((0+1)+5)*4
0146: (0+1)*(4*6)
0147: (7-(0+1))*4
0148: (4-(0+1))*8
0155: ((5*5)-1)+0
0156: (5-(0+1))*6
0226: ((0+2)+2)*6
0234: (0+2)*(3*4)
0236: ((0+2)+6)*3
0238: (0*2)+(3*8)
0239: (0+2)*(3+9)
0244: ((0+2)+4)*4
0246: (0*2)+(4*6)
0248: (8-(0+2))*4
0257: (0+2)*(5+7)
0258: (5-(0+2))*8
0266: (6-(0+2))*6
0268: ((6*8)/2)+0
0269: ((0+2)*9)+6
0288: ((0+2)*8)+8
0334: ((0+3)+3)*4
0335: ((0+3)+5)*3
0337: (0+3)+(3*7)
0338: (0*3)+(3*8)
0339: ((3*9)-3)+0
0344: (0+3)*(4+4)
0346: (0*3)+(4*6)
0348: (0*4)+(8*3)
0349: (9-(0+3))*4
0358: (0*5)+(8*3)
0359: ((0+3)*5)+9
0366: ((0+3)*6)+6
0367: (7-(0+3))*6
0368: (6-(0+3))*8
0378: (0*7)+(8*3)
0388: (0*8)+(8*3)
0389: ((8*9)/3)+0
0445: (0+4)+(4*5)
0446: (0*4)+(4*6)
0447: ((4*7)-4)+0
0448: ((0+4)*4)+8
0456: (0*5)+(6*4)
0466: (0*6)+(6*4)
0467: (0*7)+(4*6)
0468: (8-(0+4))*6
0469: (0*9)+(4*6)
0478: (7-(0+4))*8
0488: ((0+4)*8)-8
0566: ((0+5)*6)-6
0569: (9-(0+5))*6
0588: (8-(0+5))*8
0689: (9-(0+6))*8
0699: (0+6)+(9+9)
0789: (0+7)+(8+9)
0888: (0+8)+(8+8)
1118: ((1+1)+1)*8
1126: ((1+1)+2)*6
1127: (1+2)*(7+1)
1128: ((1*1)+2)*8
1129: (1+2)*(9-1)
1134: (1+1)*(3*4)
1135: (1+3)*(5+1)
1136: ((1+1)+6)*3
1137: ((1*1)+7)*3
1138: ((3*8)-1)+1
1139: (1+1)*(3+9)
1144: ((1+1)+4)*4
1145: ((1*1)+5)*4
1146: ((4*6)-1)+1
1147: (7-(1*1))*4
1148: (8-(1+1))*4
1149: (1-4)*(1-9)
1155: ((5*5)*1)-1
1156: (5-(1*1))*6
1157: (1+1)*(5+7)
1158: (5-(1+1))*8
1166: (6-(1+1))*6
1168: 8/((1+1)/6)
1169: ((1+1)*9)+6
1188: ((1+1)*8)+8
1224: (1+2)*(2*4)
1225: (1+5)*(2+2)
1226: (1+2)*(2+6)
1227: (7-1)*(2+2)
1228: (2-(1-2))*8
1229: ((1+2)+9)*2
1233: (1+3)*(3*2)
1234: ((1+2)+3)*4
1235: ((1+2)+5)*3
1236: (3-(1-2))*6
1237: (1+2)+(3*7)
1238: (2-1)*(3*8)
1239: (3*9)-(1+2)
1244: (1+2)*(4+4)
1245: (5-(1-2))*4
1246: (2-1)*(4*6)
1247: ((1-2)+7)*4
1248: ((1-2)+4)*8
1249: (9-(1+2))*4
1255: ((5*5)-2)+1
1256: ((1-2)+5)*6
1257: (1*2)*(5+7)
1258: ((5+8)-1)*2
1259: ((1+2)*5)+9
1266: ((1+2)*6)+6
1267: (7-(1+2))*6
1268: (6-(1+2))*8
1269: ((1*2)*9)+6
1277: ((7*7)-1)/2
1278: (1+7)+(8*2)
1279: ((9*2)-1)+7
1288: ((1*2)*8)+8
1289: 9/((1+2)/8)
1333: (1+3)*(3+3)
1334: ((1+3)+4)*3
1335: ((1*3)+5)*3
1336: (6-(1-3))*3
1337: ((3*7)*1)+3
1338: ((1+8)*3)-3
1339: (1+3)*(9-3)
1344: (4-(1-3))*4
1345: (1+3)+(4*5)
1346: 6/(1-(3/4))
1347: (4*7)-(1+3)
1348: ((1+3)*4)+8
1349: (9-(1*3))*4
1356: (1+5)+(6*3)
1357: (3-1)*(5+7)
1358: ((1-3)+5)*8
1359: ((1*3)*5)+9
1366: ((1-3)+6)*6
1367: (7-(1*3))*6
1368: (8-(1+3))*6
1369: 6-((1-3)*9)
1377: (1-7)*(3-7)
1378: (7-(1+3))*8
1379: (1+7)*(9/3)
1388: ((1+3)*8)-8
1389: ((8*9)/3)*1
1399: (9-1)*(9/3)
1444: ((1+4)*4)+4
1445: ((4*5)*1)+4
1446: ((1+6)*4)-4
1447: ((4*7)*1)-4
1448: ((1*4)*4)+8
1449: ((1-4)+9)*4
1455: ((5*4)-1)+5
1456: 4/(1-(5/6))
1457: ((7*4)-5)+1
1458: (1+5)*(8-4)
1459: 9-((1-4)*5)
1466: ((1+4)*6)-6
1467: ((1-4)+7)*6
1468: ((1-4)+6)*8
1469: (9-(1+4))*6
1477: (1+7)*(7-4)
1478: (7-(1*4))*8
1479: (1-9)*(4-7)
1488: (8-(1+4))*8
1489: 9/((4-1)/8)
1555: (5-(1/5))*5
1556: (5*6)-(1+5)
1559: (1+5)*(9-5)
1566: ((1*5)*6)-6
1567: ((5*6)-7)+1
1568: ((1-5)+8)*6
1569: (9-(1*5))*6
1578: ((1-5)+7)*8
1579: (1-7)*(5-9)
1588: ((5-1)*8)-8
1589: (9-(1+5))*8
1599: (1+5)+(9+9)
1666: ((6-1)*6)-6
1668: 6/(1-(6/8))
1669: ((1-6)+9)*6
1679: (1+7)*(9-6)
1688: ((1-6)+8)*8
1689: (1+6)+(8+9)
1699: ((9+9)*1)+6
1779: (1+7)+(7+9)
1788: (1+7)+(8+8)
1789: ((8+9)*1)+7
1799: ((9+9)-1)+7
1888: ((8+8)*1)+8
1889: ((8+9)-1)+8
2223: (2+2)*(2*3)
2224: ((2+2)+2)*4
2225: ((2*5)+2)*2
2227: ((2*7)-2)*2
2228: ((2+2)+8)*2
2229: ((2+9)*2)+2
2233: (2+2)*(3+3)
2234: ((2+2)+4)*3
2235: ((5*2)-2)*3
2236: ((2/2)+3)*6
2237: ((3+7)+2)*2
2238: ((3*8)-2)+2
2239: (2+2)*(9-3)
2244: ((2*4)+4)*2
2245: (2+2)+(4*5)
2246: ((4*6)-2)+2
2247: (4*7)-(2+2)
2248: ((2+2)*4)+8
2249: ((4+9)*2)-2
2255: ((5+5)+2)*2
2256: ((5+6)*2)+2
2257: (2*5)+(7*2)
2258: ((5+8)*2)-2
2259: ((5+9)-2)*2
2266: (2+6)*(6/2)
2267: ((6+7)*2)-2
2268: (8-(2+2))*6
2269: ((9*2)-6)*2
2277: ((7+7)-2)*2
2278: (7-(2+2))*8
2288: ((2+2)*8)-8
2289: ((9*2)-2)+8
2333: ((2+3)+3)*3
2335: ((3*5)-3)*2
2336: (3-(2-3))*6
2337: (7-(2-3))*3
2338: (3-2)*(3*8)
2339: ((2+3)*3)+9
2344: ((2+3)*4)+4
2345: (5-(2-3))*4
2346: (3-2)*(4*6)
2347: ((2-3)+7)*4
2348: ((2-3)+4)*8
2349: ((4*9)/3)*2
2355: ((5*5)-3)+2
2356: ((2-3)+5)*6
2357: ((7*3)-2)+5
2358: ((3+5)*2)+8
2359: (2*3)*(9-5)
2366: ((2+3)*6)-6
2367: ((6*7)/2)+3
2368: ((3*6)-2)+8
2369: (9-(2+3))*6
2377: (2*7)+(7+3)
2378: ((7+8)-3)*2
2379: ((7+9)/2)*3
2388: (8-(2+3))*8
2389: (9-(2*3))*8
2399: (2*3)+(9+9)
2444: (4-(2-4))*4
2445: ((2+5)*4)-4
2446: ((4+6)*2)+4
2447: (2*4)*(7-4)
2448: (2+4)*(8-4)
2449: ((9-2)*4)-4
2455: ((5+5)*2)+4
2456: (5*6)-(2+4)
2457: (4-2)*(5+7)
2458: ((5*8)/2)+4
2459: (2+4)*(9-5)
2466: ((2-4)+6)*6
2467: ((7*4)-6)+2
2468: ((6+8)*2)-4
2469: 6-((2-4)*9)
2477: ((7+7)*2)-4
2478: ((7*8)/2)-4
2479: (2*4)+(7+9)
2488: 8-((2-4)*8)
2489: (9-(2+4))*8
2499: (2+4)+(9+9)
2557: (2*7)+(5+5)
2558: ((5/5)+2)*8
2559: 9-((2-5)*5)
2566: 6-((2-5)*6)
2567: ((2-5)+7)*6
2568: ((2-5)+6)*8
2569: (6/(2/5))+9
2577: (2*5)+(7+7)
2578: ((2*5)-7)*8
2579: (5*7)-(2+9)
2588: (8*5)-(2*8)
2589: (2+5)+(8+9)
2666: ((6*6)/2)+6
2667: ((6*7)+6)/2
2668: ((2-6)+8)*6
2669: (2+6)*(9-6)
2678: ((2-6)+7)*8
2679: (2+6)+(7+9)
2688: (2+6)+(8+8)
2689: ((2*6)-9)*8
2699: ((9+9)-6)*2
2778: (2+7)+(7+8)
2788: ((2-7)+8)*8
2789: ((9+7)*2)-8
2888: ((8+8)*2)-8
2889: ((2-8)+9)*8
2899: ((9+9)-2)+8
3333: ((3*3)*3)-3
3334: ((3+4)*3)+3
3335: (3*3)+(3*5)
3336: (3+3)+(3*6)
3337: (3+3)*(7-3)
3338: ((3+3)-3)*8
3339: (9-(3/3))*3
3344: (3*4)+(4*3)
3345: ((4+5)*3)-3
3346: ((4*6)-3)+3
3347: ((4+7)-3)*3
3348: (3+3)*(8-4)
3349: ((9-4)+3)*3
3355: (5*5)-(3/3)
3356: (5*6)-(3+3)
3357: ((3*5)-7)*3
3359: (3+3)*(9-5)
3366: ((6/3)+6)*3
3367: ((7*3)-3)+6
3368: ((3*3)-6)*8
3369: (3*3)+(6+9)
3377: ((3/7)+3)*7
3378: (3*3)+(7+8)
3379: ((7*9)/3)+3
3388: 8/(3-(8/3))
3389: (9-(3+3))*8
3399: (3+3)+(9+9)
3444: ((3+4)*4)-4
3445: (5-(3-4))*4
3446: (4-3)*(4*6)
3447: ((3-4)+7)*4
3448: ((3+4)-4)*8
3449: (4*9)-(3*4)
3455: ((5*5)-4)+3
3456: ((3-4)+5)*6
3457: (3*4)+(5+7)
3458: ((8-5)+3)*4
3459: ((9-5)+4)*3
3466: (3*4)+(6+6)
3468: ((3*4)-8)*6
3469: ((9-6)+3)*4
3477: ((7*4)-7)+3
3478: 8-((3-7)*4)
3479: (3*4)*(9-7)
3489: (3+4)+(8+9)
3499: ((9+9)/3)*4
3556: ((5+5)*3)-6
3557: (5-3)*(5+7)
3558: ((3+5)-5)*8
3559: ((9/5)+3)*5
3566: ((3-5)+6)*6
3567: ((6+7)-5)*3
3568: 8/((5-3)/6)
3569: (3+5)*(9-6)
3578: ((8-5)*7)+3
3579: (3+5)+(7+9)
3588: (3+5)+(8+8)
3589: ((8-5)*9)-3
3599: (9/(3/5))+9
3666: 6-((3-6)*6)
3667: ((3-6)+7)*6
3668: ((3+6)-6)*8
3669: (3+6)+(6+9)
3677: ((7/7)+3)*6
3678: (3+6)+(7+8)
3679: ((9-7)+6)*3
3688: ((8/8)+3)*6
3689: 9/((6-3)/8)
3699: ((9/9)+3)*6
3777: (3+7)+(7+7)
3778: ((3+7)-7)*8
3779: (9-(7/7))*3
3788: ((7-3)*8)-8
3789: ((9-8)+7)*3
3799: ((9/9)+7)*3
3888: ((3+8)-8)*8
3889: (3*8)*(9-8)
3899: (3*8)+(9-9)
3999: ((9+9)-3)+9
4444: (4+4)+(4*4)
4445: ((4/4)+5)*4
4446: ((4+4)-4)*6
4447: (4+4)*(7-4)
4448: (4*8)-(4+4)
4449: ((9-4)*4)+4
4455: ((5+5)-4)*4
4456: (5-(4/4))*6
4457: ((7-5)+4)*4
4458: ((4+4)-5)*8
4468: ((8-6)+4)*4
4469: (4+4)*(9-6)
4477: (4-(4/7))*7
4478: ((8-4)*7)-4
4479: (4+4)+(7+9)
4488: (4+4)+(8+8)
4489: (9*4)-(4+8)
4555: ((5*5)-5)+4
4556: ((4+5)-5)*6
4557: (7-(5/5))*4
4558: (4-(5/5))*8
4559: ((9-5)*5)+4
4566: ((6/6)+5)*4
4567: ((7-6)+5)*4
4568: ((4+5)-6)*8
4569: (4+5)+(6+9)
4577: ((7/7)+5)*4
4578: (4+5)+(7+8)
4579: ((9-5)*7)-4
4588: ((8/8)+5)*4
4589: ((9-8)+5)*4
4599: ((9/9)+5)*4
4666: ((4+6)-6)*6
4667: (4*6)*(7-6)
4668: (4+6)+(6+8)
4669: 6-((4-6)*9)
4677: (4+6)+(7+7)
4678: ((4+6)-7)*8
4679: ((7+9)/4)*6
4688: 8-((4-6)*8)
4689: ((8*9)/4)+6
4699: (4*6)+(9-9)
4777: (7-(7/7))*4
4778: ((7-8)+7)*4
4788: ((4+7)-8)*8
4789: 9/((7-4)/8)
4799: (7-(9/9))*4
4888: ((8*8)/4)+8
4889: ((4+8)-9)*8
4899: (4-(9/9))*8
5555: (5*5)-(5/5)
5556: (5*5)+(5-6)
5559: (5+5)+(5+9)
5566: ((5+5)-6)*6
5567: (5*5)+(6-7)
5568: (5+5)+(6+8)
5577: (5+5)+(7+7)
5578: ((5+5)-7)*8
5588: (5*5)-(8/8)
5589: (5*5)+(8-9)
5599: (5*5)-(9/9)
5666: (5-(6/6))*6
5667: (5+6)+(6+7)
5668: 6-((5-8)*6)
5669: (6*9)-(5*6)
5677: (5-(7/7))*6
5678: ((7-8)+5)*6
5679: 6-((5-7)*9)
5688: ((5+6)-8)*8
5689: ((8-9)+5)*6
5699: (5-(9/9))*6
5779: (5+7)*(9-7)
5788: 8-((5-7)*8)
5789: ((5+7)-9)*8
5888: (5*8)-(8+8)
5889: 9/((8-5)/8)
6666: (6+6)+(6+6)
6668: ((6+6)-8)*6
6669: ((9-6)*6)+6
6679: (6+6)*(9-7)
6688: 6/((8-6)/8)
6689: ((6+6)-9)*8
6789: (6*8)/(9-7)
6799: (6*7)-(9+9)
6888: 8-((6-8)*8)
6889: (8*9)-(6*8)
6899: ((9+9)/6)*8
7889: 8-((7-9)*8)

Thanks!

[JPF]

Here is one I made with my program... I found 466 possible cases (out of 715 total combinations of 4 numbers from 0 to 9)... It'd be very appreciated if someone else could verify this figure with another program...

I agree with the list of the 466 numbers.
I didn't check the formula...

So the next question is : what are the numbers with a unique solution ?
To be precise , let's agree that for 1235 :
((1+2)+5)*3
3*((2+1)+5)
are the same solution.

What do you think ?

JPF

[udosuk]

That's exactly the question I'm working at - the grand prize of 10000 points...

I could program out the duplications described by you, but there are other "implicit" duplications which are hard to pick out, e.g.

(3-1)*9+6
6-(1-3)*9

(8/2)*7-4
7/(2/8)-4

Should we consider them as duplicates?

It seems a pretty good computing assignment to write a program to find all the combinations with unique formulas... Perhaps I should post this in the programming forum...

[underquark]

Via deze pagina kunt u 4x6-Oplossingen downloaden. Met dit programma kunt u alle oplossingen zoeken voor "4x6-game". Doel van het spel is om met 4 willekeurige getallen bijvoorbeeld de uitkomst 24 te vinden door de 4 getallen te delen/op te tellen/af te trekken/te vermenigvuldigen. Klik hieronder op "download" om het programma op te slaan. Met MinUnzip kunt u het programma uitpakken.

See:
http://home.planet.nl/~edejong/4x6-oplossingen/home.html

[JPF]

I could program out the duplications described by you, but there are other "implicit" duplications which are hard to pick out, e.g.

(3-1)*9+6
6-(1-3)*9

(8/2)*7-4
7/(2/8)-4

Should we consider them as duplicates?

If * is an operation :
"x*y" is equivalent to "y*x" if * is a commutative operation.
(in addition x*y=y*x, by definition).

Let's write "x*y"~"y*x"

So :
"1+2" ~ "2+1"
"(1+2)+5" ~ "5+(2+1)"

and

"3*((2+1)+5)" ~ "(5+(1+2))*3"

"3*((2+1)+5)" and "(5+(1+2))*3" are duplicates

but :

"(3-1)*9+6" is not equivalent to "6-(1-3)*9"

and therefore

"(3-1)*9+6 " and "6-(1-3)*9" are two different solutions.

JPF

[JPF]

I found 37 numbers with a unique solution :

Code: Select all

1118
1169
1188
1277
1346
1555
1666
1668
2225
2227
2229
2235
2258
2449
2455
2477
2558
2578
2789
3333
3339
3357
3366
3377
3388
3444
3779
4445
4477
4557
4558
4599
4777
4799
4899
5666
5677


It'd be very appreciated if someone else could verify this figure ...
(for the solutions, see udosuk's previous post)

For 1,4,5,6 :

Code: Select all

1456 : 4/(1-(5/6)) = 24

What about :

Code: Select all

1456 : 6/((5/4)-1) = 24

which is not equivalent.

JPF

[udosuk]

JPF, I don't think your list is comprehensive enough... For example:

4*4+4+4
5*5-5/5

Should be included in the list... Probably more...

It's a big challenge to write a 100% working program... I wish some of the solver programmers could take this up...

[JPF]

JPF, I don't think your list is comprehensive enough... For example:
4*4+4+4
5*5-5/5

You are right : 5555 should be part of the list.

But not 4444 :
In my opinion, (4*4)+(4+4) and ((4*4)+4)+4 are 2 different solutions.
In one case we add 16+8 and in the other one 16+4 and 20+4.

We need first to agree on the definitions

JPF

[udosuk]

Let's first define what structure we're doing with... I reckon the Algebraic Field is a good one...

You've decided to adopt the commutative property, so why not pick the associative property too?

For all a, b, c in F, a + (b + c) = (a + b) + c and a * (b * c) = (a * b) * c.

However, it might make the programming trickier...

For example:

(7+9)+(9-1)
(7+9)-(1-9)
(7-1)+(9+9)
(9-1)+(7+9)

You might want to define them as different, but IMO they're all the same:
7+9+9-1

[JPF]

You might want to define them as different, but IMO they're all the same

OK, udosuk ; even if you are not #9, you are the boss in this thread.

However, it might make the programming trickier...

Let's try.

JPF

[udosuk]

Still working at it...

A few weeks ago, I was #9 and not the boss...

Now the boss is #9 and I'm the boss in this thread...

Strange turnaround...