# Melbourne University Mathematics and Statistics Society

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 Solution for 4.4 Trends (Answer = DALTON)

The main part of this puzzle consists of a series of stars in six colours in an apparently random arrangement. By searching for some of the numbers in the stars, we should quickly notice that they are atomic weights of chemical elements. This combines with the title "Trends" to indicate six different trends of the Periodic Table.

At the bottom of the puzzle we can see six two letter codes. By looking at a list of chemical properties we can see that these codes indicate the trends we need to use: Atomic Radius, Boiling Point, Electronegativity, Heat Capacity, Ionisation Energy and Melting Point.

We now need to connect the six colours to the six trends. Along with the two letter codes we six groups of four dot-delimited numbers. These can be interpreted as colours under the CMYK model used for print documents, suggested by the first hint "The numbers at the end might make more sense if you print out the page." and the second half of the second hint "Everything in this puzzle has to do with elements. How can you represent a colour using four numbers from 0 to 100?".

The last step is to use the trends to order the stars. By connecting stars of each colour according to the associated trend we can draw six letters. The whole process was described in the third hint "Atomic Radius is one of the trends in the periodic table, so use this to order the stars (which represent elements) that have the same CMYK number as AR. You will need to anagram these 6 letters for the final answer, but the D obtained from Atomic Radius will be the first letter."

Details of these steps are given in the table below.

 Periodic Trend CMYK Atomic Weight Element Trend value Join the dots AR (Atomic Radius) 7.52.0.36 32.07 S 1.80 D (Purple) 127.60 Te 2.06 107.87 Ag 2.11 22.99 Na 2.27 140.12 Ce 2.42 BP (Boiling Point) 70.32.0.28 14.01 N 77.355 N (Blue) 200.59 Hg 629.769 10.81 B 4273 101.07 Ru 4420 190.23 Os 5281 EN (Electronegativity) 0.48.76.35 39.10 K 0.82 O (Brown) 87.62 Sr 0.95 54.94 Mn 1.55 112.41 Cd 1.69 131.29 Xe 2.60 15.99 O 3.44 HC (Heat Capacity) 0.33.100.0 30.97 P 23.824 A (Orange) 63.55 Cu 24.44 208.98 Bi 25.52 88.91 Y 26.53 207.20 Pb 26.65 IE (Ionisation Energy) 56.0.58.31 223.00 Fr 392.96 L (Green) 26.98 Al 577.539 72.64 Ge 762.179 126.90 I 1008.393 79.90 Br 1139.859 MP (Melting Point) 0.89.88.11 74.92 As 889 T (Red) 151.96 Eu 1095 9.01 Be 1560 55.85 Fe 1811 91.22 Zr 2127 183.84 W 3687

Anagramming the six letters gives us the final answer DALTON, best known for his work on the development of atomic theory.

Note: There is no definitive way to display CMYK colours, in particular they can change depending on the web page or editing program used. In solving the puzzle you may have noticed that the colours given by the CMYK values do not exactly match what is shown in the image. This caused the puzzle to go through several iterations choosing different sets of colours. In the final version we tried to use a set that would be unambiguous so that if you found a green it would be clear which stars it referred to even if the colour was not an exact match. The CMYK values came from a conversion website (colorizer.org) as we thought more teams were likely to use this than an editing program such as photoshop.