M51 arithmetic

henryzz · 2019-01-06, 17:14

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

LaurV · 2019-01-06, 17:37

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)

Brownfox · 2019-01-06, 17:38

4 = 8+2+5+8-9-9-(3/3)

science_man_88 · 2019-01-06, 17:55

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

henryzz · 2019-01-06, 18:27

22 = 8+2*(5+8)-9-9+3+3

Brownfox · 2019-01-06, 18:34

26 = 8+(2*5)+8+9-9+3-3
27 = 8+(2*5)+8-9+9+(3/3)

LaurV · 2019-01-07, 06:13

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...

henryzz · 2019-01-07, 09:45

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

axn · 2019-01-07, 10:47

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

science_man_88 · 2019-01-07, 11:11

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.

science_man_88 · 2019-01-07, 11:29

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.

2019-01-06, 17:37	#2
LaurV Romulan Interpreter Jun 2011 Thailand 9369₁₀ Posts	4 = 8/2+5899(3-3) 5 = 8+2-5+899(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

2019-01-07, 10:47	#9
axn Jun 2003 17³ 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+58+9-9-33 Last fiddled with by axn on 2019-01-07 at 10:54

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

2019-01-06, 17:38	#3
Brownfox Dec 2017 3²×7 Posts	4 = 8+2+5+8-9-9-(3/3)

2019-01-06, 18:27	#5
henryzz Just call me Henry "David" Sep 2007 Cambridge (GMT/BST) 5,857 Posts	22 = 8+2*(5+8)-9-9+3+3

2019-01-06, 18:34	#6
Brownfox Dec 2017 3²×7 Posts	26 = 8+(25)+8+9-9+3-3 27 = 8+(25)+8-9+9+(3/3)