Welcome Math Horizons readers! Our puzzles from the September 2024 issue are available here, with hints at the bottom of the page.

Want to learn more about Mathematical Puzzle Programs, and how to get your community engaged in ideas from contemporary mathematics?  Email us at info@MaPPmath.org to connect!

“Welcome to MaPP University! Go Pigeons!”

It’s your first day on the grounds, and it seems they weren’t kidding at orientation: pretty much everything is turning out to be a puzzle! As shown on the cover, you see castles guarded by strange statues, manually operated lamp posts, and oversized dice arranged on grids, each of which apparently encodes a secret word. Your mind wanders back to your college tour, when your guide said mysteriously, “It’s said that those who can see how these three secret words are intertwined within the MaPP University motto can also see our motto’s true meaning: ADDISUPM UPCASLOCAO QLMSRAOM.” That’s no kind of Latin you’re familiar with, but fortunately the spelling (and a specific arrangement of letters) is displayed on a sign next to Metapuzzle Hall. Your first class isn’t for a couple of hours, so you and a friend decide to work on the puzzles together...

MOTTO: _ _ _ _ _ _ _

You spend a few minutes watching the dean rolling dice across the twelve large grids in front of Metapuzzle Hall, muttering “all that matters is the pips one can see.” Apparently, one of the secret words is named after a location where they love to play such dice games.

After some thought, your friend realizes that there’s a way that the lower die in grid A could be moved into the upper die’s position: south, east, north, north, east, north, west, south, east, north, west, south, east. Can you find another? But try as you both might, there’s no way this could be accomplished with the dice in grid T. There’s got to be a simpler way to see which rolls are possible and which are not...

DICE: _ _ _ _

Your friend once heard that the university’s founder, Sir Mappington Pigeonhole, was a huge patron of the arts. In fact, the lamp posts installed on the MaPP University courtyard are arranged in the exact same layout as the chandeliers in his favorite art gallery, with the gallery’s walls represented as lines drawn on the ground.

Always a frugal man, Sir Pigeonhole used electricity sparingly. You wonder, assuming light cannot pass over a boundary, if Sir Pigeonhole were to illuminate his art gallery using the least number of lights, which of the lights could NOT be used?

LAMP POSTS: _ _ _ _ _ _

Long ago, MaPP University erected three castles with statues of soldiers standing guard on several of their towers. The four crests on the statue’s shields represent the four MaPP University schools: the Dashing School of Science (–), the Wedgington School of Technology (∧), the Nablanian School of Engineering (∇), and the Boxuto School of Mathematics (☐).  Each castle had certain guard restrictions.

If a castle is guarded by a school, that school must be represented by at least two statues.

Statues with the – crest must be exactly distance one apart (that is, in adjacent towers) from all other statues sharing their crest; statues with the ∧ crest must be exactly distance two; statues with the ∇ crest must be exactly distance three; and statues with the ☐ crest must be exactly distance four.

As the legend goes, students from a rival school stole several of the statues that originally stood guard according to these rules. Each remaining statue is represented by its crest in the illustration below, while each statue-less tower is associated with a letter of the alphabet. Your friend suspects that these castles are the key to another secret word: you just need to figure out how to add back as many statues as possible to the remaining towers, while following the above rules...

Errata: Despite the cover illustration, it is not required to have a ☐ guard in position H of the leftmost castle.

CASTLES: _ _ _ _ _ _ _ _ _

Hints

Copy-paste into ROT13.com to decipher these hints:

• MOTTO

  • Guvf vf n zrgn-chmmyr, fb lbh fubhyq jnvg gb fbyir guvf hagvy nsgre lbh'ir fbyirq gur bgure guerr chmmyrf.

  • Gur bayl arprffnel ryrzrag bs gur pbire vyyhfgengvba hfrq va guvf chmmyr vf gur neenatrzrag bs gur yrggref NQQVFHCZ HCPNFYBPNB DYZFENBZ ba gur fvta.

  • Rnpu bs gur guerr fbyhgvbaf sbe gur bgure chmmyrf nccrnef "guernqrq" jvguva gur yrggref ba guvf fvta. Gurfr yrggref jvyy abg or hfrq va gur zrgnchmmyr fbyhgvba.

• DICE

  • Gurer ner bayl sbhe cbffvoyr ebyyf bhg bs gur gjryir cerfragrq. Gurfr jvyy erirny gur sbhe yrggref bs gur chmmyr'f fbyhgvba.

  • Lbh pbhyq teno n qvr naq fgneg ebyyvat vg nebhaq, ohg gurer'f npghnyyl n fyvpx jnl gb svther bhg juvpu pbasvthengvbaf ner cbffvoyr, naq juvpu ner abg. "Nyy gung znggref vf gur cvcf bar pna frr."

  • Jung unccraf gb gur fhz bs cvcf ba n qvr jura lbh ebyy vg rknpgyl bar fcnpr?

  • Ebyyvat n qvr bar fcnpr rkpunatrf na bqq inyhrq snpr jvgu na rira inyhrq snpr, be ivpr irefn. Pna lbh hfr gung gb qvfpbire gur sbhe cbffvoyr ebyyf?

• LAMP POSTS

  • Gur neg tnyyrel pna or vyyhzvangrq hfvat svir yvtugf (naq ab yrff).

  • Gurer ner fvk yvtugf gung, vs gurl ner hfrq, cerirag gur neg tnyyrel sebz orvat vyyhzvangrq hfvat svir yvtugf gbgny. Gurfr tvir gur fvk yrggref bs gur fbyhgvba.

  • Lbh'yy arrq gb hfr bar yvtug sbe rnpu bs gur svir iregvpny unyyjnlf. Jung fvk yvtugf erznva?

• CASTLES

  • Gurer ner bayl gjb hahfrq fcnprf va gur yrsgzbfg pnfgyr. Lbh jvyy abg hfr nal fgnghrf sebz Obkhgb.

  • Va gur yrsgzbfg pnfgyr lbh pna vafreg gjb zber fgnghrf sebz Qnfuvat, bar zber sebz Jrqtvatgba, naq gjb zber sebz Anoynavna.

  • Gb trg gur avar gbgny yrggref, lbh'yy arrq gjb yrggref sebz gur yrsg pnfgyr, sbhe sebz gur zvqqyr pnfgyr, naq guerr sebz gur evtug pnfgyr.

  • Gur zvqqyr pnfgyr qbrf abg unir nal gbjref qvfgnapr guerr be ybatre sebz bar nabgure, fb Anoynavna naq Obkhgb jvyy abg or hfrq gurer. Gur evtug pnfgyr jvyy hfr nyy sbhe perfgf, ubjrire.

Still stuck? Email us at info@mappmath.org!