# SolveMe Mobiles: "Puzzler" difficulty

Going further:

This and the other "Going further" section, refer to problems which are not offered by the SolveMe Mobiles website. These are questions I consider interesting, usually somewhat more abstract than solving some particular mobile. Here's the first such question: Can you solve the puzzle below, if only the value of the hexagon is given?

Yes. Label the strands A, B, C, from left to right. Strand A is 5, while strands B and C are each 2 1/2. We know the value for strands B and C, and all but one shape, in each case. Thus, we can determine the droplet and diamond shapes. What if we were given the value of some other shape or shapes at the start? Notice that the value of the entire mobile is given, and every pair of distinct shapes occurs as a strand. That is,

• (droplet, diamond)
• (hexagon, droplet)
• (diamond, hexagon)

Thus, if we know one of the shapes, we can figure out one of the strands, which tells us the value of another shape, and this chain continues until all shapes are known.

Strategy 10:

The total of the middle strand can only be determined if the left strand, right strand, and subtree totals are known. For example, in the puzzle below, the right strand must be 6, the left strand must then also be 6, and so the middle strand must be 20 - 12 = 8.

Going further:

Label the strands in the puzzle below A, B, C, D, from left to right.

Without doing any calculation, in what order would you determine the value of each strand? C first, A second, B and D third. That is, it doesn't matter whether B is found before D, or vice-versa.

Strategy 11:

If the value of the middle strand, and the value of its subtree are known, then reduce the value of the subtree by the value of the middle strand, and mentally remove the middle strand from the puzzle.