# Fill the holes? [closed]

You have to fill the boxes to make the equation true:

+   +   = 30

Using only 1, 3, 5, 7, 9, 11, 13, 15.

You can also repeat the numbers. (eg: 1 + 1 + 1)

### Edit 2:

That's my first post here and I didn't realize how fantastics your mind was, that's why my question was so broad. I'll accept the answer I was expecting but it doesn't mean that the other are wrong. Let's the upvoter decide.

• Can you use other operators e.g. (3-1) + (5*7) + ... Apr 8, 2015 at 15:26
• This puzzle is essentially "guess what trick I am thinking of". There are plenty of tricks/loopholes that could be used, and no real way to determine which one is "correct". xkcd.com/169 Apr 8, 2015 at 15:40
• I don't see any boxes. Apr 8, 2015 at 15:47
• @BenFrankel the boxes deflated to an underline as there's nothing holding it up. Thomas should put '?' in it, or he can't do it for a reason =)
– Alex
Apr 8, 2015 at 16:46
• Do any of the base-$x$ solutions answer the question to your satisfaction? Apr 9, 2015 at 3:16

__+15+15 = 30

Assuming we don't need to use all the boxes

• I think you have to fill in all the boxes as the question stated
– Alex
Apr 8, 2015 at 15:40
• Look at the comments under Alex's answer. Seems like maybe we can only use 2. Apr 8, 2015 at 15:52
– Alex
Apr 8, 2015 at 16:11
• @Thomas a wiki quote: The plus sign (+) is a binary operator that indicates addition, as in 2 + 3 = 5. It can also serve as a unary operator that leaves its operand unchanged (+x means the same as x). You can't have a plus sign alone. Apr 9, 2015 at 11:54
• I think "15+15+" isn't a valid mathematical expression, but I think "+15+15" would be. Apr 9, 2015 at 11:58

15 + 115 + 135 == 110 + 610 + 810 == 1510 == 305
35 + 115 + 115 == 310 + 610 + 610 == 1510 == 305
17 + 117 + 157 == 110 + 810 + 1210 == 2110 == 307
17 + 137 + 137 == 110 + 1010 + 1010 == 2110 == 307
37 + 117 + 137 == 310 + 810 + 1010 == 2110 == 307
57 + 117 + 117 == 510 + 810 + 810 == 2110 == 307
19 + 139 + 159 == 110 + 1210 + 1410 == 2710 == 309
39 + 119 + 159 == 310 + 1010 + 1410 == 2710 == 309
39 + 139 + 139 == 310 + 1210 + 1210 == 2710 == 309
59 + 119 + 139 == 510 + 1010 + 1210 == 2710 == 309
79 + 119 + 119 == 710 + 1010 + 1010 == 2710 == 309
111 + 1511 + 1511 == 110 + 1610 + 1610 == 3310 == 3011
311 + 1311 + 1511 == 310 + 1410 + 1610 == 3310 == 3011
511 + 1111 + 1511 == 510 + 1210 + 1610 == 3310 == 3011
511 + 1311 + 1311 == 510 + 1410 + 1410 == 3310 == 3011
711 + 1111 + 1311 == 710 + 1210 + 1410 == 3310 == 3011
911 + 1111 + 1111 == 910 + 1210 + 1210 == 3310 == 3011
313 + 1513 + 1513 == 310 + 1810 + 1810 == 3910 == 3013
513 + 1313 + 1513 == 510 + 1610 + 1810 == 3910 == 3013
713 + 1113 + 1513 == 710 + 1410 + 1810 == 3910 == 3013
713 + 1313 + 1313 == 710 + 1610 + 1610 == 3910 == 3013
913 + 1113 + 1313 == 910 + 1410 + 1610 == 3910 == 3013
515 + 1515 + 1515 == 510 + 2010 + 2010 == 4510 == 3015
715 + 1315 + 1515 == 710 + 1810 + 2010 == 4510 == 3015
915 + 1115 + 1515 == 910 + 1610 + 2010 == 4510 == 3015
915 + 1315 + 1315 == 910 + 1810 + 1810 == 4510 == 3015
717 + 1517 + 1517 == 710 + 2210 + 2210 == 5110 == 3017
917 + 1317 + 1517 == 910 + 2010 + 2210 == 5110 == 3017
919 + 1519 + 1519 == 910 + 2410 + 2410 == 5710 == 3019

Edit: a cool idea from Ian MacDonald.

A better answer would only use bases that match the allowed numbers ;)

113 + 115 + 1515 == 4 + 6 + 20 == 30
113 + 117 + 1315 == 4 + 8 + 18 == 30
113 + 117 + 1513 == 4 + 8 + 18 == 30
113 + 119 + 1115 == 4 + 10 + 16 == 30
113 + 119 + 1313 == 4 + 10 + 16 == 30
113 + 119 + 1511 == 4 + 10 + 16 == 30
113 + 1111 + 1113 == 4 + 12 + 14 == 30
113 + 1111 + 1311 == 4 + 12 + 14 == 30
113 + 1111 + 159 == 4 + 12 + 14 == 30
113 + 1113 + 139 == 4 + 14 + 12 == 30
113 + 1113 + 157 == 4 + 14 + 12 == 30
113 + 1115 + 137 == 4 + 16 + 10 == 30
113 + 135 + 1315 == 4 + 8 + 18 == 30
113 + 135 + 1513 == 4 + 8 + 18 == 30
113 + 137 + 1313 == 4 + 10 + 16 == 30
113 + 137 + 1511 == 4 + 10 + 16 == 30
113 + 139 + 1311 == 4 + 12 + 14 == 30
113 + 139 + 159 == 4 + 12 + 14 == 30
113 + 1311 + 157 == 4 + 14 + 12 == 30
113 + 157 + 159 == 4 + 12 + 14 == 30
115 + 115 + 1315 == 6 + 6 + 18 == 30
115 + 115 + 1513 == 6 + 6 + 18 == 30
115 + 117 + 1115 == 6 + 8 + 16 == 30
115 + 117 + 1313 == 6 + 8 + 16 == 30
115 + 117 + 1511 == 6 + 8 + 16 == 30
115 + 119 + 1113 == 6 + 10 + 14 == 30
115 + 119 + 1311 == 6 + 10 + 14 == 30
115 + 119 + 159 == 6 + 10 + 14 == 30
115 + 1111 + 1111 == 6 + 12 + 12 == 30
115 + 1111 + 139 == 6 + 12 + 12 == 30
115 + 1111 + 157 == 6 + 12 + 12 == 30
115 + 1113 + 137 == 6 + 14 + 10 == 30
115 + 1115 + 135 == 6 + 16 + 8 == 30
115 + 135 + 1313 == 6 + 8 + 16 == 30
115 + 135 + 1511 == 6 + 8 + 16 == 30
115 + 137 + 1311 == 6 + 10 + 14 == 30
115 + 137 + 159 == 6 + 10 + 14 == 30
115 + 139 + 139 == 6 + 12 + 12 == 30
115 + 139 + 157 == 6 + 12 + 12 == 30
115 + 157 + 157 == 6 + 12 + 12 == 30
117 + 117 + 1113 == 8 + 8 + 14 == 30
117 + 117 + 1311 == 8 + 8 + 14 == 30
117 + 117 + 159 == 8 + 8 + 14 == 30
117 + 119 + 1111 == 8 + 10 + 12 == 30
117 + 119 + 139 == 8 + 10 + 12 == 30
117 + 119 + 157 == 8 + 10 + 12 == 30
117 + 1111 + 137 == 8 + 12 + 10 == 30
117 + 1113 + 135 == 8 + 14 + 8 == 30
117 + 135 + 1311 == 8 + 8 + 14 == 30
117 + 135 + 159 == 8 + 8 + 14 == 30
117 + 137 + 139 == 8 + 10 + 12 == 30
117 + 137 + 157 == 8 + 10 + 12 == 30
119 + 119 + 119 == 10 + 10 + 10 == 30
119 + 119 + 137 == 10 + 10 + 10 == 30
119 + 1111 + 135 == 10 + 12 + 8 == 30
119 + 135 + 139 == 10 + 8 + 12 == 30
119 + 135 + 157 == 10 + 8 + 12 == 30
119 + 137 + 137 == 10 + 10 + 10 == 30
1111 + 135 + 137 == 12 + 8 + 10 == 30
1113 + 135 + 135 == 14 + 8 + 8 == 30
135 + 135 + 1311 == 8 + 8 + 14 == 30
135 + 135 + 159 == 8 + 8 + 14 == 30
135 + 137 + 139 == 8 + 10 + 12 == 30
135 + 137 + 157 == 8 + 10 + 12 == 30
137 + 137 + 137 == 10 + 10 + 10 == 30

Plus many more if we also allow base ten on the LHS, ex. 11 + 115 + 13 == 11 + 6 + 13 == 30

• Not only "beat," but kick, stomp, stamp, jump, crush, and spit. Nicely done! Apr 8, 2015 at 15:00
• A better answer would only use bases that match the allowed numbers. ;) Apr 9, 2015 at 12:18
• @IanMacDonald, ok, I've added those too :-) I think 30 should remain in base 10, though, since 1) there's no "box" on the right hand side where I could put a new base; and 2) If I listed all the solutions where 30 is in a different base, this answer would be a lot longer. Apr 9, 2015 at 12:49

I think we can use a little trick:

Just use 9 upside down: 11 + 6 + 13 = 30

• Not what I expected but I can't say a firm no Apr 8, 2015 at 14:20
• @Thomas hah, but for real answer are we expected to use all the boxes or?
– Alex
Apr 8, 2015 at 14:25
• The answer to your question is in my question... :) Apr 8, 2015 at 14:27

The sum of 3 odd numbers will always be odd, so there is no answer that will yield an even number

• Exactly what I was going to say. Well done! Apr 8, 2015 at 16:07
• But then it wouldn't be a puzzle then would it? :| Apr 8, 2015 at 16:45

I can solve this puzzle as a physicist:

15 + 15 + 1 = 30

I guess it's more reasonable to request a precise mathematical 30 however..

The only boxes I see are the ones around 1,...,15...
I can fill the boxes like so: 10, 10, 10, 10, 10, 10, 10, 10.

And then the problem becomes trivial.

13 + 15 + 1 = 30 in base 9.

This isn't formatted the way I want, I'll go learn how to do that properly and come back to edit later.

• It doesn't... Or maybe I made a mistake but I find (9+4)+(9+6)+1 which is 29 Apr 8, 2015 at 14:36
• @Thomas If you convert all to base-10, 13->12, 15->14, 1->1 Apr 8, 2015 at 14:39
• The operands and result are all base 9. Apr 8, 2015 at 14:45

The solution is:

11+13+1=30 in base 5

Note that the text doesn't specify the base of the equation.

• 11+3+1 => 20 (in base 5) not 30 Apr 8, 2015 at 14:38
• By my reckoning, 1 + 11 + 13 in base 5 equals 1 + 6 + 8 in base 10, which equals 15 in base 10, which equals 30 in base 5. Apr 8, 2015 at 14:39
• @Kevin I didn't see it that way :) Apr 8, 2015 at 14:40
• @Kevin yes, but the answer used 3, not 13 Apr 8, 2015 at 15:04
• Oops :-) I need to work on my reading comprehension. Apr 8, 2015 at 15:05

I am aware that the word equation implies that L should be equal R, but what if...

..it is sufficient to "make the equation true" by filling the boxes? ..or do I need to make the equation correct as well?