M51 arithmetic

[retina]

Originally Posted by uau

for example 31415926 fails at 607 already.

666 = 3*1*4*1*5*(9+2)+6

[uau]

Originally Posted by retina

666 = 43112609 ??

((4*3+1/(1+2))*6+0)*9
Other "??" aren't possible.

[retina]

Originally Posted by uau

((4*3+1/(1+2))*6+0)*9
Other "??" aren't possible.

I found another also

666 = 4*3*(1+1/2+6*(0+9))

Using the 1/2 was the key it seems. I couldn't find any without a fractional component.

[uau]

Originally Posted by retina

I couldn't find any without a fractional component.

I checked that on the computer with the program changed to reject some fractional results, and yes it's not possible without an intermediate fraction of either x/2 or x/3.

[retina]

666 = 3*(0-(2+1))*(3-77)
666 = -(2+0-9)*(96+0-1)+1
666 = 3*(0-4+0-2+4*57)

[henryzz]

Some more solutions for the last 4 digits:

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

I can't solve 14 or 16. I suspect they aren't possible.

What do people think to allowing notation such as the following?
117 to 120 = 8*(2+5+8) - L4D[3 to 0]
121 to 133 = 8*(2+5+8) + L4D[1 to 13]

It is fairly clear and saves a lot of typing and mistakes.

[retina]

Originally Posted by henryzz

Some more solutions for the last 4 digits:

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

I can't solve 14 or 16. I suspect they aren't possible.

What do people think to allowing notation such as the following?
117 to 120 = 8*(2+5+8) - L4D[3 to 0]
121 to 133 = 8*(2+5+8) + L4D[1 to 13]

It is fairly clear and saves a lot of typing and mistakes.

So with a stride of 27 (-13 to +13) we only need to find the first four digit values.

130 = (8+2)*(5+8)
144 = 8*(2*5+8)
160 = 8/(2/(5*8))
168 = (8*2+5)*8
192 = 8*(2-5)*8
208 = 8*2*(5+8)
<222 to 226 not covered>
240 = (8-2)*5*8
<254+ not covered>

So we can fill in the gaps:
222 = 8*2*(5/(8/(9*9/3))-3)
223 = 8+2*5*(8+9*9/(3+3)) -- Also can be 208+15
224 = 8*2*(5+8+9-(9-3/3))
225 = 8/(2/(5/(8/(9+9*3*3)))) -- I especially like this one with all the divisions, also can be 240-15
226 = 8*2*(5+8+9/(9-3/3))

[retina]

With the following suffixes we can span a stride of 9 (-4 to +4)

0 = 9-3*3
1 = 9/3/3
2 = (9-3)/3
3 = 9-3-3
4 = (9+3)/3

And with the following prefixes we can cover 251 to 274 inclusive

255 = (8+2+5)*(8+9)
261 = (8*2+5+8)*9
264 = 8*(2+5*8-9)
268 = -8/(2/(5-8*9))
270 = -(8+2-5*8)*9

[henryzz]

Feel free to use the ones that we have >13 or >4. Any additions to those lists may turn out to be useful.
If results could be posted using the notation I am using in the 1st post that would save me some time.

I have added:
8 = 9-3/3
9 = 9+3-3
10 = 9+3/3 to the L3D list

[retina]

Originally Posted by henryzz

I have added:
8 = 9-3/3
9 = 9+3-3
10 = 9+3/3 to the L3D list

Also:

6 = 9/3+3

[retina]

275 = 8*2+5+8+9*9*3+3