# What's the smallest chemical elements word search that can be made?

I want the elements from 1 to 118, their names, atomic numbers and symbols including capitalization.

There is one important rule that makes things a little more difficult:

No item can be completely contained within a single other.

So single letter symbols must be on their own square that doesn't overlap anything else. Multiple letter (or number) items can overlap completely with other items so long as they overlap more than one.

Here's an example of a valid grid with just H and He (and their names and numbers):

Hydrogen
2muileH1
H???????


So it's okay that He overlaps the e in Hydrogen and the H in Helium because although it is completely contained in other words, it is contained in more than one.

This is an example of a bad grid using the same items:

Hydrogen
e12?????
l???????
i???????
u???????
m???????


It's bad because both H and He are completely contained within Helium. That they also overlap Hydrogen doesn't matter because they are completely contained by an item.

As stated in the title I want the smallest grid (by area) and in the event of two answers having the same area the one that is closest to being square wins.

In the unlikely event that both have the same dimensions then the grid that has the most unused squares will be the winner. (if even that ties then I'll count the number of extra occurrences of each item)

Provide your answers as text so I can copy and paste it into a testing program.

Unused square can be filled in or left blank as you see fit.

Here's a list of the items to use:

1 H Hydrogen 2 He Helium 3 Li Lithium 4 Be Beryllium 5 B Boron 6 C Carbon 7 N Nitrogen 8 O Oxygen 9 F Fluorine 10 Ne Neon 11 Na Sodium 12 Mg Magnesium 13 Al Aluminium 14 Si Silicon 15 P Phosphorus 16 S Sulfur 17 Cl Chlorine 18 Ar Argon 19 K Potassium 20 Ca Calcium 21 Sc Scandium 22 Ti Titanium 23 V Vanadium 24 Cr Chromium 25 Mn Manganese 26 Fe Iron 27 Co Cobalt 28 Ni Nickel 29 Cu Copper 30 Zn Zinc 31 Ga Gallium 32 Ge Germanium 33 As Arsenic 34 Se Selenium 35 Br Bromine 36 Kr Krypton 37 Rb Rubidium 38 Sr Strontium 39 Y Yttrium 40 Zr Zirconium 41 Nb Niobium 42 Mo Molybdenum 43 Tc Technetium 44 Ru Ruthenium 45 Rh Rhodium 46 Pd Palladium 47 Ag Silver 48 Cd Cadmium 49 In Indium 50 Sn Tin 51 Sb Antimony 52 Te Tellurium 53 I Iodine 54 Xe Xenon 55 Cs Caesium 56 Ba Barium 57 La Lanthanum 58 Ce Cerium 59 Pr Praseodymium 60 Nd Neodymium 61 Pm Promethium 62 Sm Samarium 63 Eu Europium 64 Gd Gadolinium 65 Tb Terbium 66 Dy Dysprosium 67 Ho Holmium 68 Er Erbium 69 Tm Thulium 70 Yb Ytterbium 71 Lu Lutetium 72 Hf Hafnium 73 Ta Tantalum 74 W Tungsten 75 Re Rhenium 76 Os Osmium 77 Ir Iridium 78 Pt Platinum 79 Au Gold 80 Hg Mercury 81 Tl Thallium 82 Pb Lead 83 Bi Bismuth 84 Po Polonium 85 At Astatine 86 Rn Radon 87 Fr Francium 88 Ra Radium 89 Ac Actinium 90 Th Thorium 91 Pa Protactinium 92 U Uranium 93 Np Neptunium 94 Pu Plutonium 95 Am Americium 96 Cm Curium 97 Bk Berkelium 98 Cf Californium 99 Es Einsteinium 100 Fm Fermium 101 Md Mendelevium 102 No Nobelium 103 Lr Lawrencium 104 Rf Rutherfordium 105 Db Dubnium 106 Sg Seaborgium 107 Bh Bohrium 108 Hs Hassium 109 Mt Meitnerium 110 Ds Darmstadtium 111 Rg Roentgenium 112 Cn Copernicium 113 Uut Ununtrium 114 Fl Flerovium 115 Uup Ununpentium 116 Lv Livermorium 117 Uus Ununseptium 118 Uuo Ununoctium

• Um.. isn't "H" completely contained in a few different other words? How would a player know which "H" is a standalone? – Ian MacDonald Jun 26 '15 at 15:19
• I haven't checked but does your word search meet the criteria? I.E., can we use that as an upper bound? – Engineer Toast Jun 26 '15 at 15:19
• @IanMacDonald My understanding is that it is OK so long as the is standalone somewhere. For instance, a 3x3 grid of Q with H in the middle is clearly a standalone H. So long as there is at least one solution in which all terms are found, it's OK. – Engineer Toast Jun 26 '15 at 15:20
• 118x3 means the possibilities are almost endless. This is an enormous puzzle. – JLee Jun 26 '15 at 15:20
• @EngineerToast correct about the rules, as for my previous puzzle I'm not sure it would be valid but it had tons of unused space that could have been used to make it fit the rules. I think I made a few smaller ones which didn't get saved. If think 36x36 was my best but that was with a pseudo-random algorithm that wasn't very efficient at packing. – Bob Jun 26 '15 at 15:30

EDIT: A new submission in which I have high confidence.

## Method

1. Use an online program to densely pack the element names
2. Dump the contents into Excel
3. Use my previously-written VBA script to highlight the element names
4. Remove all non-highlighted characters
5. Manually search for any element symbols already highlighted. Make sure they're not fully contained within a single other item and watch out for symbols using the same letters like Sc and Cs.
6. Manually fill in any remaining symbols using the white space. This was Uuo, Uup, all of the single-character symbols (14), and less than 10 of the others (I forgot to count).
7. Manually fill in the atomic numbers using the white space remaining

## Results

44 rows $\times$ 23 columns $=$ 1,012 total characters
147 filler characters $\Rightarrow$ 85.5% utilization

## Puzzle

14501N44224126014?C8915
01mmMeitnerium103oa70m6
211u1Neodymium10pBl7nuL
n32ii05mbmEinsteiniumiU
om0t6m1uuicU??rs??fSvtT
runn31yiNnu?nnmmX?oeLe5
oiMolybdenumiuu??erarn3
Bn?rtrProtactiniumnb2h3
oe?tEpwoneihnoIooBio8c2
iun3l26eKiRiru8u16iis01
uRi45l7hTUnZmPi115Au9H8
mIr9muitnepnunU178rmmy2
FFo2m?muiveledneMos??dI
relZu?nRm??gHmuihtemorP
arheitmulatnaTnp95nuool
nmCnrrKManganese35intgu
cimieocnegyxOoe986caSet
iuumC?voVWe3h4p8m4sheno
umnoA?RinYNP79tuus8tl2n
muiramaSuiAluminiumne7i
uitB??eStmu??suusNuan5u
inaYtterbiumoRmiemiLimm
nalFluorineru??pnurouuu
bmPArgon8cpb?Tt?giuimii
ur?Ae6736simmuidallaPds
De?nC694yd?unn??Melobae
?GmtoG9Di?iimg?Cbke?dna
?muiporuEdum?s?oLrT?iaC
??implm?nmmoItNb?eht?VG
??toed?a?uurTe?a?Barium
yUenr?c?miihhn?lmtldm??
1rty?SG?uddCu??tsuluup?
2au??i?aional??Actinium
3nLc?l?ulSIlim?nNnurh??
4i??rvm?el?cu?iCoSmmt??
5u?C?e??H?iimZalOcuPit?
6m?u?rM???muidohRiilL?Y
7??rNickelimmP??n?slfC?
8??iCarbonSi???e?Osmium
9??u???HfmuirohT??a??Sr
???muidaRm???R????H????
??????H????????????????


## Solution

Element names are highlighted. Fillers are left blank. Anything in the white space was manually added to finish out whatever was missing.

• I'll be posting some JavaScript code to let people check their submission later. Did you work this out by hand? – Bob Jun 26 '15 at 17:46
• I only worked out the numbers by hand. I intend to next work out the symbols by hand to see if I can manually pack it more densely. – Engineer Toast Jun 26 '15 at 18:52
• I'd love to be able to offer some sage advice, but to be honest I set this question because I hadn't had any really good ideas for solving it myself and wondered how others would do. – Bob Jun 26 '15 at 19:06