This week ’s brain teaser will boldly go where no puzzle has gone before . Try and keep up .
This week ’s puzzle was created byUniversity of Kentucky mathematician Raphael Finkel , and commend by io9 referee Shahab Tasharrofi . ” I create the puzzle as a exam caseful for some software I write that assists puzzle Maker , ” Finkel tell me when I asked for his permission to feature the puzzle in our weekly puzzle series . “ I wanted to sample out some pretty complex clues that my software handles . ” He adds : “ I conceive , by the way , that this puzzler is extremely difficult . ”
Challenge accepted .
Sunday Puzzle #10: Six Fearsome Heroes
Grobly Grizik is planning to publish a novel forge after Star Trek : The Next Generation . In this novel , six of the crew members contend both atFizzbinand atTridimensional chess game . Each crew phallus develop two main rankings for ability at these plot , with 1 ranked last and 6 mellow . Every crew appendage has a personal submarine sandwich among the crew , and every crowd phallus is afraid of some crew appendage . Everyone is the hero of somebody , and everyone is fear by somebody . Nobody either fears him / herself nor counts him / herself as a hero . Nobody fears his / her own hero . From the render clues , discover every crew phallus ’s ranking at Fizzbin and at Tri - five hundred chess game , as well as whom he / she fears and whom he / she counts as a hero :
Geordi ranks 2 at Tri - D Chess .
Picard rate two position behind Troi at Fizzbin .
Troi is feared by the person Geordi venerate .
Worf ’s fighter ranks 3 time low at Tri - D Chess than the crew extremity who is best at Fizzbin .
Picard ’s Cuban sandwich fears Geordi .
Data ’s torpedo is not Geordi .
Data is the hero of Riker ’s hero .
The mortal who is worst at Fizzbin is good than Troi at Tri - D Chess .
The person rate number 3 at Tri - D Chess is ranked 4 position higher than Data at Fizzbin .
Riker is feared by the person Picard fears and is the hero of Worf ’s Cuban sandwich .
Riker is rank 2 lower at Tri - D Chess than the crew penis ranked 2 at Fizzbin .
We ’ll be back next calendar week with the solution – and a raw puzzle ! Got a great brainteaser , original or otherwise , that you ’d wish to see featured?E - get off me with your recommendations.(Be certain to include “ Sunday Puzzle ” in the subject line . )
graphics by Jim Cooke
UPDATE:THE SOLUTION TO THE STAR TREK PUZZLE HAS BEEN POSTED
Solution To Sunday Puzzle #9: The Puzzle Of 100 Hats
Last calendar week , I asked you to save the lives of as many hat - wearing prisoner as you could . One of the jot I provided was that you could deliver a stack more than 50 of the 100 lives on the line . In fact , I order , the just plan would definitely save 99 lives , and leave behind only one life to encounter .
100 life Are On The channel In This Week ’s Puzzle . How Many Can You Save ?
Right aside , several of you seized on a solution to this problem involving pitch contour that , I include , is a passably clever workaround . Xilonen03was the first to provide this alternative solution and commit , I suppose , the clearest explanation for how it would be comport out :
I ’d simply have the last someone in dividing line announce the color of the hat of the 99th person . Person 100 has a 50 % chance of living , but from there on out , everyone can live . Person 99 now knows the people of colour of their lid , and hopefully it ’s not covered in blood spatter . If the color of their lid matches that of the soul in front of them , they will announce the colour as a statement ; if the people of color of their hat does not match that of the person in front of them , they will announce their colour as a question .
So it would look something like this :
100 : Red . ( person 99 ’s hat is cherry-red )
99 : Red ? ( someone 98 ’s hat is downcast )
98 : Blue . ( person 97 ’s hat is blue )
97 : Blue ? ( soul 96 ’s chapeau is red )
etc etc etc …
I actually really like this solution . It ’s quite ingenious . But it ’s not the result I was bet for . And , in fact , many of you pointed outthat Xilonen03 ’s solution kind of outrage the look of the puzzler , which is mean to be lick with logical system , and need not be left to either the execution or rendering of outspoken quirks .
The first somebody to provide the solvent we were search for wasNiro1 , who wrote :
The answer below allows 99 prisoners to judge their chapeau color mighty with sure thing .
the last prisoner in the pillar counts the number of crimson lid in front of him ( he can see all the other 99 ) if he realize an singular bit of bolshie he shout out RED and if he sees an eve number of red he shout BLUE . the next person and all the other captive after that can deduce their color and shout the correct number .
For example lets assume that prisoner 99 has a red lid , 98 has a red hat and 97 has a downhearted hat and completely there are 46 blue hats and 53 reds :
Prisoner 100 get word 53 red hats so he scream RED .
prisoner number 99 sees only 52 ruby hats ( he ca nt see the one on his own head ) which is an even number but prisoner 100 shouted RED for an remaining number of reds so there is one red chapeau omit so he have sex he is wearing a red hat .
Prisoner 98 sees only 51 red hat but he he do it that captive 100 saw an odd number of reds and prisoner 99 already shouted red so he should see an even number but he catch 51 ( an odd number ) so again one crimson hat is missing – the one on his foreland .
Prisoner 97 is expect to see an odd number of red ( because we started with an odd number of reds and 2 hoi polloi behind him already said they are endure red hats ) and indeed he sees 51 violent hats – so he shouts BLUE
And so on …
Northeastern University math prof Terence Gaffneyhas some helpful adviceon how to simplify , solve , and interpret problem of this nature :
One hundred captive are too many to knead with . Suppose there are two . The last mortal can save the guy in front of him by shouting out the coloring of his chapeau . OK , how about if there are three ? The third prisoner can see 0,1 , or 2 blue hats . There seem to be three possibility but only two choices of thing to say . But , two of the possibilities have something in common – namely the figure of drab hats is even . So if the last prisoner yells “ naughty ” then he can differentiate # 1 and # 2 that he sees an even number of blueish hats . Then the second prisoner , by looking in advance and counting the number of blue hat , knows his must be blue if he see one low lid , and blood-red if he sees no blue hats . The last captive agrees to yell “ red ” if the phone number of aristocratic hats see is odd . Then if # 2 sees a dingy chapeau on # 1 , his must be violent , and if # 1 has a red chapeau , his must be blue . By shouting out the colour of his hat , # 1 also knows his hat color . Two “ wild blue yonder ” or two “ reds ” in a row mean he wears gamey , while one blue and one Marxist means he wears red . OK . This calculate like this always works , because there are always only two hypothesis as far as the number of blue hats worn – they are either even or odd . So , check out as in the three person subject that using this strategy ( “ blue ” for an even number of bluish hats “ red ” for an odd number ) tells # 99 the color of his hat , and then each prisoner in turn can learn the color of his hat by taking into account the parity of the turn of blue hat he can see , the mirror symmetry of the number of blue hats # 100 saw and the number of captive behind him wearing blue hats .
Remember : puzzler like this one can seem grown and unwieldy at first coup d’oeil , but can often be simplified . ( Think back to the100 Green - Eyed Dragonspuzzle . ) When approaching a new puzzle , always ask yourself : Have you seen this or a related problem before ? Have you find out a similar unknown before ? Can you restate the job ? If you ca n’t work this problem , can you puzzle out a like or simpler problem ?
Previous Weeks’ Puzzles
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Think You get it on The Solution To This Classic Riddle ? imagine Again .
“ The Hardest Logic Puzzle In The public ”
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Star Trek
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