mersenneforum.org M51 arithmetic
 Register FAQ Search Today's Posts Mark Forums Read

 2019-01-06, 17:14 #1 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 16EE16 Posts M51 arithmetic Most of us will have heard of the 4 4s puzzle where you try to create numbers using only the number 4 and various operators. Mersenneforum has multiple threads where variants have been explored. Having discovered it again so soon after a new Mersenne prime has been found I thought it would be a fun challenge to use the numbers from the new exponent 82,589,933. Initially it would be nice to keep it simple just using the operators +, -, * and / along with brackets to see how far we can get. Other operators will be added later once they are needed(maybe a scoring system could be worked out). All digits must be used. Bonus points(I suspect it will be too hard very quickly) for using the digits in the correct order. I will start us off with a few examples: Code: 0 = (8+2+5+8+9+9)*(3-3) 1 = 8-2+5+8-9-9+3-3 2 = 8-2+5+8-9-9+(3/3) 3 = 8-2+5-8-9+9+3-3 edit: Solutions so far: Code: 0 = (8+2+5+8+9+9)*(3-3) 1 = 8-2+5+8-9-9+3-3 2 = 8-2+5+8-9-9+(3/3) 3 = 8-2+5-8-9+9+3-3 4 = 8/2+5*8*9*9*(3-3) 5 = 8+2-5+8*9*9*(3-3) 6 = 8+2-5-8+9+9*(3-3) 7 = 8+2+5-8-9+9-3+3 8 = 8+2*5*8*9*9*(3-3) 9 = (8-2-5+8)*(9/9)*(3/3) 10 = (8-2)+(5+8-9*(9/(3*3)) 11 = (8+2)/5 + 8+(9/9)*(3/3) 12 = (8+2-5)+8*(9/9)-(3/3) 13 = (8+2-5)+8*(9/9)*(3/3) 14 = (8+2-5)+8*(9/9)+(3/3) 15 = (8+2-5)+8+9/9+3/3 16 = (8+2+5-8+9)*(9/(3*3)) 17 = (8+2+5-8+9+(9/(3*3)) 18 = (8-2-5)*(8+9)+(9/(3*3)) 19 = (8-2-5)+(8+9)+(9/(3*3)) 20 = 8+2+5+(8-9)+(9/3)+3 21 = (8+2+5-8)*(9/(9-3-3)) 22 = (8+2+5+8)-(9/9)*(3/3) 23 = (8+2+5+8)*(9/9)*(3/3) 24 = (8+2+5+8)+(9/9)*(3/3) 25 = ((8+2)*5)-8-9-9+(3/3) 26 = (8*2+5+8)-(9/(9-3-3)) 27 = (8*2+5+8)-(9/9)-(3/3) 28 = (8*2+5+8)-((9/9)*(3/3)) 29 = (8*2+5+8)*(9/9)*(3/3) 30 = (8*2+5+8)+((9/9)*(3/3)) 31 = (8*2+5+8)+(9/9)+(3/3) 32 = (8+2+5+8+9)*(9/(3*3)) 33 = (8+2+5+8+9)+(9/(3*3)) 34 = 8-2+5+8+9+9/3+3 35 = 8+2+5+8+9+9-3-3 36 = 8-2+5+8+9+9-3/3 37 = 8-2+5*8+9-9-3*3 38 = 8+2+5+8+9+9/3+3 39 = (8+2)*5-8-9+(9/3)+3 40 = (8+2)*5-8-(9/9)-(3/3) 41 = (8+2)*5-8-((9/9)*(3/3)) 42 = (8+2)*5-8+(9/9)-(3/3) 43 = (8+2)*5-8+((9/9)*(3/3)) 44 = (8+2)*5-8+(9/9)+(3/3) 45 = (8+2)*5-8+(9/(9-3-3)) 46 = (8+2+5+8)*((9/9)+(3/3)) 47 = 8+2+5+8+9+9+3+3 48 = 8*(2+5+8-9)*(9/(3*3)) 49 = (8+2+5-8)*((9/9)+3+3) 50 = (8+2)*5+8-9+9/3/3 51 = (8+2)*5-8+9*9/3/3 52 = (8+2)*5-8+9+9/3/3 53 = 8 * 2 * 5 - 8 - 9 - 9 - 3/3 54 = 8 * 2 * 5 - 8 - 9 - 9 - (3 - 3) 55 = 8 * 2 * 5 - 8 - 9 - 9 + 3/3 56 = 8 * 2 + 5 * 8 - 9/9 + 3/3 57 = (8+2)*5+8-(9/9*3/3) 58 = (8+2)*5+8+(9-9+3-3) 59 = (8+2)*5+8 + (9/9*3/3) 60 = (8+2)*5+8 + (9/9+3/3) 61 = (8+2)*5+8 + (9-9/3-3) 62 = (8+2)*5+8 + ((9+9/3)/3) 63 = (8+2)*5+8 - (9/9-3-3) 64 = (8+2)*5+8 + (9-9+3+3) 65 = (8+2)*5+8 + (9/9+3+3) 66 = (8+2)*5+8 + (9-9/3/3) 67 = (8+2)*5+8 + (9*9/3/3) 68 = (8+2)*5+8 + (9+9/3/3) 69 = ((8 - 2 + 5 + 8 + (9/9) + 3)) * 3 70 = (8-2)*(5+8)-(9-9/3/3) 71 = (8-2)*(5+8)-(9/9+3+3) 72 = (8-2)*(5+8)-(9-9+3+3) 73 = (8-2)*(5+8)+(9/9-3-3) 74 = (8-2)*(5+8)-((9+9/3)/3) 75 = (8-2)*(5+8)-(9-9/3-3) 76 = (8-2)*(5+8)-(9/9+3/3) 77 = (8-2)*(5+8)-(9/9*3/3) 78 = (8-2)*(5+8)-(9-9+3-3) 79 = (8-2)*(5+8)+(9/9*3/3) 80 = (8-2)*(5+8)+(9/9+3/3) 81 = (8-2)*(5+8)+(9-9/3-3) 82 = (8-2)*(5+8)+((9+9/3)/3) 83 = (8-2)*(5+8)-(9/9-3-3) 84 = (8-2)*(5+8)+(9-9+3+3) 85 = (8-2)*(5+8)+(9/9+3+3) 86 = (8-2)*(5+8)+(9-9/3/3) 87 = (8-2)*(5+8)+(9*9/3/3) 88 = (8-2)*(5+8)+(9+9/3/3) 89 = (8-2-5)*8+(9*9)*(3/3) 90 = 8*2*5 + 8 + 9/9 + 3/3 91 = (8*2*5/8)*9 +9/3/3 92 = 8*2*5+8+((9+9/3)/3) 93 = 8*2*5+8-(9/9-3-3) 94 = 8*2*5+8-9+9+3+3 95 = 8*2*5+8+9/9+3+3 96 = 8*2*5-8+9+9+3+3 97 = (8+2)*(5+8+9-9-3)-3 98 = -8-2+(5+8)*9-9+3-3 99 = 8/2+5+8+9*9+3/3 100 = 8+2-5+8+9*9+3+3 101 = 8*2+5+8+9*9-3*3 102 = 8*(2+5+8)-9-9+3-3 103 = (8+2)*(5+8+9-9-3)+3 104 = -8+(2*5)+(8*9)+(9*3)+3 105 = 8+2+5*(8+9+(9-3)/3) 106 = 8-2+5+8+9*9+3+3 107 = 8+(2×5−8+9)×9−3+3 108 = 8+2*5+8+9*9+3/3 109 = 8*2-5+8+9*9+3*3 110 = 8*2+5+8+9*9+3-3 111 = 8-2+5*(8+9+(9+3)/3) 112 = -8+2+5*(8+9+9-3)+3 113 = 8+2+5*(8+9+9/3)+3 114 = -8/2+5*(8+9+9-3)+3 115 = 8+2+5*(8+9+(9+3)/3) 116 = 8*2+5*(8+9+9-3-3) 117 to 133 = 8*(2+5+8) + L4D[-3 to 13] 134 to 143 = (8+2)*(5+8) + L4D[4 to 13] 144 to 157 = 8*(2*5+8) + L4D[0 to 13] 158 to 173 = 8/(2/(5*8)) + L4D[-2 to 13] 174 to 181 = (8*2+5)*8 + L4D[6 to 13] 182 to 205 = 8*(2-5)*8 + L4D[-10 to 13] 206 to 221 = 8*2*(5+8) + L4D[-2 to 13] 222 = 8*2*(5/(8/(9*9/3))-3) 223 = 8+2*5*(8+9*9/(3+3)) 224 = 8*2*(5+8+9-(9-3/3)) 225 = 8/(2/(5/(8/(9+9*3*3)))) 226 = 8*2*(5+8+9/(9-3/3)) 227 to 253 = (8-2)*5*8 + L4D[-13 to 13] 254 to 259 = (8+2+5)*(8+9) + L3D[-1 to 4] 260 to 265 = (8+2+5)*(8+9) + L3D[-1 to 4] 266 to 268 = (8+2+5)*(8+9) + L3D[2 to 4] 269 to 273 = (8+2+5)*(8+9) + L3D[1 to 4] 274 = (8+2+5)*(8+9) + L3D[4] 275 = 8*2+5+8+9*9*3+3 276 = (8-2)*5*8+9*(9+3)/3 277 = 8*(2*(5+8)+9) + L3D[-3] 278 = (8-2)*5+8+9*9*3-3 279 = -(8+2-5*8)*9 + L3D[9] 280 = 8+2*(5+8)+9*9*3+3 281 = 8*(2*(5+8)+9) + L3D[1] 282 = (8+2)*5-8+9*9*3-3 283 = (8*2)*(5+8)+9*9-3-3 284 = 8*(2*(5+8)+9) + L3D[4] 285 to 292 = (8-(2-5)*8)*9 + L3D[-3 to 4] 293 to 298 = (8-2)*(5*8+9) + L3D[-1 to 4] 299 to 317 = 8*(-2+5*8) + L4D[-13 to 13] 318 to 319 = 8*(2+5*8) + L4D[-18 to -17] 320 = 8*2*5*(8-L4D[4]) 321 = 8*(2+5*8) + L4D[-15] 322 = 8*(-2+5*8) + L4D[18] 323 to 349 = 8*(2+5*8) + L4D[-13 to 13] 350 to 356 = 8*2*(5+8+9) + L3D[-3 to 4] 357 = 8-2+5*8*9 + L3D[-9] 358 = -8+2+5*8+9*(9+3)*3 359 = -8/2+5*8*9 + L3D[3] 360 = 8-2+5*8*9+L3D[-6] 361 = 8+2+5*8*9+L3D[-9] 362 to 370 = 8-2+5*8*9 + L3D[-4 to 4] 371 to 374 = 8+2+5*8*9 + L3D[1 to 4] 375 to 380 = 8*2+5*8*9 + L3D[-1 to 4] 381 = (8+2)*5*8 + L4D[-19] 382 to 390 = 8+(2+5*8)*9 + L3D[-4 to 4] 391 to 413 = (8+2)*5*8 + L4D[-9 to 13] 414 to 418 = (8-2+5*8)*9 + L3D[0 to 4] 419 = (8+2)*5*8 + L4D[19] 420 = (8-2+5*8)*9 + L3D[6] 421 = (8+2)*5*8 + L4D[21] 422 to 424 = (8-2+5*8)*9 + L3D[8 to 10] 425 = 8+2+5*(8+9*9-3-3) 426 = ((8+2)+5*8)*9 - 9*3+3 427 = 8*(2+5)*8 + L4D[-21] 428 = (-8+(2+5)*8)*9 +L3D[-4] 429 to 431 = 8*(2+5)*8 + L4D[-19 to -17] 432 = 8/2*(5+8)*9 - (9+3)*3 433 = 8*(2+5)*8 + L4D[-15] 434 to 461 = 8*(2+5)*8 + L4D[-13 to 13] 462 = 8/2*(5+8)*9 + L3D[-6] 463 = (8+2)*(5*8+(9+9)/3)+3 464 to 472 = 8/2*(5+8)*9 + L3D[-4 to 4] 473 = 8+2+5*(8+9*9+3)+3 474 = (8*2+5*8)*9+L3D[-30] 475 = (8+2)*(5*8+9) + L3D[-15] 476 = 8+(2+5)*8*9 + L3D[-36] 477 = 8/(2/(5+8)/9)+9-3+3 478 = 8*2*(5*8-9) + L3D[-18] 479 = (8+2)*5+8*9*(9-3)-3 480 to 482 = (8+2)*(5*8+9) + L3D[-10 to -8] 483 = 8/(2/(5+8)/9) + L3D[15] 484 = (8+2)*(5*8+9) + L3D[-6] 485 = (8+2)*5+8*9*(9-3)+3 486 to 494 = (8+2)*(5*8+9) + L3D[-4 to 4] 495 = (8*2+5*8)*9 + L3D[-9] 496 = (8+2)*(5*8+9) + L3D[6] 497 = 8*2*(5*8-9) + L3D[1] 498 to 500 = (8+2)*(5*8+9) + L3D[8 to 10] 501 to 504 = (8*2+5*8)*9 + L3D[-3 to 0] 505 = (8+2)*(5*8+9) + L3D[15] 506 to 507 = (8*2+5*8)*9 + L3D[2 to 3] 508 = (8+2)*(5*8+9) + L3D[18] 509 = (8-2)*5*(8+9) + L3D[-1] 510 = (8*2+5*8)*9 + L3D[6] 511 = 8*2*(5*8-9) + L3D[15] 512 to 513 = (8*2+5*8)*9 + L3D[8 to 9] 514 = (8+2)*(5*8+9) + L3D[24] 515 = 8+(2+5)*8*9 + L3D[3] 516 = (8-2)*5*(8+9) + L3D[6] 517 = (8+2)*(5+8)*(9/9+3)-3 518 = (8-2)*5*(8+9) + L3D[8] 519 = (8*2+5*8)*9 + L3D[15] 520 = (8+2)*(5*8+9) + L3D[30] 521 = 8+(2+5)*8*9 + L3D[9] 522 = (8*2+5*8)*9 + L3D[18] 523 = (8+2)*(5+8)*(9/9+3)+3 525 = (8-2)*5*(8+9) + L3D[15] 526 = (8+2)*(5*8+9) + L3D[36] 527 = 8+(2+5)*8*9 + L3D[15] 528 = (8*2+5*8)*9 + L3D[24] 532 = 8*2*(5*8-9) + L3D[36] 534 = (8*2+5*8)*9 + L3D[30] 536 = 8+(2+5)*8*9 + L3D[24] 540 = (8*2+5*8)*9 + L3D[36] 542 = 8+(2+5)*8*9 + L3D[30] 546 = (8-2)*5*(8+9) + L3D[36] 548 = 8+(2+5)*8*9 + L3D[36] 666 = (8*2*5-8)*9+9+3*3 Last 4 digits: Code: 0 = (9-9+3-3) 1 = (9/9*3/3) 2 = (9/9+3/3) 3 = (9-9/3-3) 4 = ((9+9/3)/3) 5 = -(9/9-3-3) 6 = (9-9+3+3) 7 = (9/9+3+3) 8 = (9-9/3/3) 9 = (9*9/3/3) 10 = (9+9/3/3) 11 = 9+(9-3)/3 12 = 9+9-3-3 13 = 9+(9+3)/3 15 = -9+9*3-3 17 = 9+9-3/3 18 = 9+9+3-3 19 = 9+9+3/3 21 = -9+9*3+3 24 = 9*9/3-3 30 = 9*9/3+3 33 = 9+9*3-3 36 = 9*(9+3)/3 39 = 9+9*3+3 Last 3 digits: Code: 0 = 9-3*3 1 = 9/3/3 2 = (9-3)/3 3 = 9-3-3 4 = (9+3)/3 6 = 9/3+3 8 = 9-3/3 9 = 9+3-3 10 = 9+3/3 15 = 9+3+3 18 = 9+3*3 24 = 9*3-3 30 = 9*3+3 36 = (9+3)*3 Last fiddled with by henryzz on 2019-02-17 at 16:59
 2019-01-06, 17:37 #2 LaurV Romulan Interpreter     Jun 2011 Thailand 24EC16 Posts 4 = 8/2+5*8*9*9*(3-3) 5 = 8+2-5+8*9*9*(3-3) 6 = 8+2-5-8+9+9*(3-3) (hehe, just ugly hack popped to my head in half second, looking at how you made zero) Last fiddled with by LaurV on 2019-01-06 at 17:41
 2019-01-06, 17:38 #3 Brownfox     Dec 2017 778 Posts 4 = 8+2+5+8-9-9-(3/3)
2019-01-06, 17:55   #4
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26×131 Posts

Quote:
 Originally Posted by LaurV 4 = 8/2+5*8*9*9*(3-3) 5 = 8+2-5+8*9*9*(3-3) 6 = 8+2-5-8+9+9*(3-3)
7=8+2+5-8-9+9-3+3
8=8+2*5*8*9*9*(3-3)
9=(8-2-5+8)*(9/9)*(3/3)
10=(8-2)+(5+8-9*(9/(3*3))
11=(8+2)/5 + 8+(9/9)*(3/3)
12=8+2-5-8+9+9+3+3
13=(8+2-5)+8*(9/9)*(3/3)
14=(8+2-5)+8*(9/9)+(3/3)
15=(8+2-5)+8+9/9+3/3
16=(8+2+5-8+9)*(9/(3*3))
17=(8+2+5-8+9+(9/(3*3))
18=(8-2-5)*(8+9)+(9/(3*3))
19=(8-2-5)+(8+9)+(9/(3*3))
20=8+2+5+(8-9)+(9/3)+3
21= (8+2+5-8)*(9/(9-3-3))
22=(8+2+5+8)-(9/9)*(3/3)
23=(8+2+5+8)*(9/9)*(3/3)
24=(8+2+5+8)+(9/9)*(3/3)
25=((8+2)*5)-8-9-9+(3/3)
26=(8*2+5+8)-(9/(9-3-3))
27=(8*2+5+8)-(9/9)-(3/3)
28=(8*2+5+8)-((9/9)*(3/3))
29=(8*2+5+8)*(9/9)*(3/3)
30=(8*2+5+8)+((9/9)*(3/3))
31=(8*2+5+8)+(9/9)+(3/3)
32=(8+2+5+8+9)*(9/(3*3))
33=(8+2+5+8+9)+(9/(3*3))
34=(8-2+5+8+9)+(9-3-3)
35=(8-2+5-8+9)+(9+3-3)
36=(8-2+5-8+9)+9+3+3

Last fiddled with by science_man_88 on 2019-01-06 at 18:37 Reason: adding a few more each edit. doh errors.

 2019-01-06, 18:27 #5 henryzz Just call me Henry     "David" Sep 2007 Cambridge (GMT/BST) 133568 Posts 22 = 8+2*(5+8)-9-9+3+3
 2019-01-06, 18:34 #6 Brownfox     Dec 2017 32×7 Posts 26 = 8+(2*5)+8+9-9+3-3 27 = 8+(2*5)+8-9+9+(3/3)
2019-01-07, 06:13   #7
LaurV
Romulan Interpreter

Jun 2011
Thailand

22×17×139 Posts

Quote:
 Originally Posted by science_man_88 34=(8-2+5+8+9)+(9-3-3) huh? 35=(8-2+5-8+9)+(9+3-3) huh? 36=(8-2+5-8+9)+9+3+3 huh?
I took it from the end, but stopped after 3 wrong out of 3... 100% failure rate...

2019-01-07, 09:45   #8
henryzz
Just call me Henry

"David"
Sep 2007
Cambridge (GMT/BST)

133568 Posts

Quote:
 Originally Posted by science_man_88 7=8+2+5-8-9+9-3+3 8=8+2*5*8*9*9*(3-3) 9=(8-2-5+8)*(9/9)*(3/3) 10=(8-2)+(5+8-9*(9/(3*3)) 11=(8+2)/5 + 8+(9/9)*(3/3) 12=8+2-5-8+9+9+3+3 13=(8+2-5)+8*(9/9)*(3/3) 14=(8+2-5)+8*(9/9)+(3/3) 15=(8+2-5)+8+9/9+3/3 16=(8+2+5-8+9)*(9/(3*3)) 17=(8+2+5-8+9+(9/(3*3)) 18=(8-2-5)*(8+9)+(9/(3*3)) 19=(8-2-5)+(8+9)+(9/(3*3)) 20=8+2+5+(8-9)+(9/3)+3 21= (8+2+5-8)*(9/(9-3-3)) 22=(8+2+5+8)-(9/9)*(3/3) 23=(8+2+5+8)*(9/9)*(3/3) 24=(8+2+5+8)+(9/9)*(3/3) 25=((8+2)*5)-8-9-9+(3/3) 26=(8*2+5+8)-(9/(9-3-3)) 27=(8*2+5+8)-(9/9)-(3/3) 28=(8*2+5+8)-((9/9)*(3/3)) 29=(8*2+5+8)*(9/9)*(3/3) 30=(8*2+5+8)+((9/9)*(3/3)) 31=(8*2+5+8)+(9/9)+(3/3) 32=(8+2+5+8+9)*(9/(3*3)) 33=(8+2+5+8+9)+(9/(3*3)) 34=(8-2+5+8+9)+(9-3-3) 35=(8-2+5-8+9)+(9+3-3) 36=(8-2+5-8+9)+9+3+3
Copied all these into excel. 12 is wrong(21) as are 34, 35, 36. The rest are right apart from unbalanced brackets in 10 and 17

 2019-01-07, 10:47 #9 axn     Jun 2003 2·13·191 Posts 34=8-2+5+8+9+9/3+3 36=8-2+5+8+9+9-3/3 EDIT:- 35=8+2+5+8+9+9-3-3 38=8+2+5+8+9+9/3+3 37=8-2+5*8+9-9-3*3 Last fiddled with by axn on 2019-01-07 at 10:54
2019-01-07, 11:11   #10
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by henryzz Copied all these into excel. 12 is wrong(21) as are 34, 35, 36. The rest are right apart from unbalanced brackets in 10 and 17
yeah I found the errors myself hence the edit reason of doh errors. 12=(8+2-5)+8*(9/9)-(3/3) though. beyond 47 addition won't work without multiplication as well.

2019-01-07, 11:29   #11
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

838410 Posts

Quote:
 Originally Posted by axn 38=8+2+5+8+9+9/3+3
39=(8*2*5)-8-9+(9/3)+3
40=(8*2*5)-8-(9/9)-(3/3)
41=(8*2*5)-8-((9/9)*(3/3))
42=(8*2*5)-8+(9/9)-(3/3)
43=(8*2*5)-8+((9/9)*(3/3))
44=(8*2*5)-8+(9/9)+(3/3)
45=(8*2*5)-8+(9/(9-3-3))
46=(8+2+5+8)*((9/9)+(3/3))
47=8+2+5+8+9+9+3+3 // combined only from here.

 Similar Threads Thread Thread Starter Forum Replies Last Post ewmayer Science & Technology 34 2015-10-03 01:31 science_man_88 science_man_88 11 2014-07-30 22:53 science_man_88 Miscellaneous Math 42 2011-07-26 02:02 mfgoode Puzzles 82 2007-05-02 08:13 R.D. Silverman Factoring 3 2006-06-05 23:49

All times are UTC. The time now is 22:39.

Sun May 16 22:39:48 UTC 2021 up 38 days, 17:20, 0 users, load averages: 1.53, 1.50, 1.55