# 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.

## closed as too broad by singletee, mdc32, Engineer Toast, Aggie Kidd, Rob WattsApr 8 '15 at 17:50

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

• Can you use other operators e.g. (3-1) + (5*7) + ... – Eamonn McEvoy Apr 8 '15 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 – singletee Apr 8 '15 at 15:40
• I don't see any boxes. – Ben Frankel Apr 8 '15 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 '15 at 16:46
• Do any of the base-$x$ solutions answer the question to your satisfaction? – Lawrence Apr 9 '15 at 3:16

## 8 Answers

__+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 '15 at 15:40
• Look at the comments under Alex's answer. Seems like maybe we can only use 2. – huddie96 Apr 8 '15 at 15:52
• There should be an option to delete under your answer after your last line in the answer – Alex Apr 8 '15 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. – Qwerty Apr 9 '15 at 11:54
• I think "15+15+" isn't a valid mathematical expression, but I think "+15+15" would be. – Kevin Apr 9 '15 at 11:58

To fully beat the "what about in other bases" dead horse,

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! – Aggie Kidd Apr 8 '15 at 15:00
• A better answer would only use bases that match the allowed numbers. ;) – Ian MacDonald Apr 9 '15 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. – Kevin Apr 9 '15 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 – Thomas Ayoub Apr 8 '15 at 14:20
• @Thomas hah, but for real answer are we expected to use all the boxes or? – Alex Apr 8 '15 at 14:25
• The answer to your question is in my question... :) – Thomas Ayoub Apr 8 '15 at 14:27

I think the answer is

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! – Allan Apr 8 '15 at 16:07
• But then it wouldn't be a puzzle then would it? :| – Sol Infinus Apr 8 '15 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 – Thomas Ayoub Apr 8 '15 at 14:36
• @Thomas If you convert all to base-10, 13->12, 15->14, 1->1 – leoll2 Apr 8 '15 at 14:39
• The operands and result are all base 9. – Ayefork Apr 8 '15 at 14:45

The solution is:

11+13+1=30 in base 5

That's valid if your numbers are in base-5 instead of base-10.
Note that the text doesn't specify the base of the equation.

• 11+3+1 => 20 (in base 5) not 30 – Thomas Ayoub Apr 8 '15 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. – Kevin Apr 8 '15 at 14:39
• @Kevin I didn't see it that way :) – Thomas Ayoub Apr 8 '15 at 14:40
• @Kevin yes, but the answer used 3, not 13 – EagleV_Attnam Apr 8 '15 at 15:04
• Oops :-) I need to work on my reading comprehension. – Kevin Apr 8 '15 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?

My answer is

1 + 1 + 1

• What's your definition for "true"? – Ben Frankel Apr 8 '15 at 15:55
• @BenFrankel As the OP stated. Filled boxes make the equation true. – Qwerty Apr 8 '15 at 15:55