//------------------------------// // Puzzle 2 solution // Story: School of Logic: a Collection of Puzzles involving the Student Six // by Coyotek4 //------------------------------// “You know, Gallus, if you put as much effort into your studies as you do in ways to get out of doing your studies …” Gallus quickly brushes off Ocellus’s observation. “Yeah yeah yeah, whatever, where do we begin?” The changeling sighs, shakes her head, and chuckles to herself. “I’m happy with getting help on this one,” she finally admits. “Well, first we need to figure out who got the score of 96. All we know for certain is that it’s not Yona.” The yak blinks. “Why Yona not get 96?” “You predicted you would get a 97,” Ocellus answers. “Now if you did get the 97, your prediction would be false; that’s a contradiction. So your prediction was false, but that means you got an odd-numbered score. Since it can’t be 97, you must have gotten either the 95 or the 99.” “Wait … Yona might have gotten high score in class? Yona happy!” Sandbar chuckles. “May have gotten the highest score. We don’t know yet.” “Fifty-fifty better than one-in-six!” Yona declares. “Whoa,” Gallus responds with a tinge of surprise, “you really do know math.” His comment causes Yona to beam. “So anyway,” Ocellus says, returning to the task at hoof, “Yona got either 95 or 99; she could not have gotten 96. Now we need to figure out who did … and the key is, knowing who got 96 must lead to a unique solution.” “Sounds good so far,” Smolder states, her thoughts drifting towards the possibility of no homework. “Now I predicted that I would not get the lowest score.” The young dragon ponders her comment for a moment. “Sooo … if I did get the lowest score, that would be a 94 … but that would mean I made a false comment with an even-numbered score, right?” Ocellus nods with an ‘mmm-hmmm’. “Cool … I guess … so that means I didn’t get the lowest score, and I made a true prediction … so I had to get either a 96 or a 98, right?” “That’s right,” Ocellus states. “One more piece of the puzzle.” “Yeah, but I think we’re out of edge pieces,” Gallus adds. Silverstream starts searching the floor around them, causing the griffin to roll his eyes. “Not literally, Silverstream!” The hippogriff gets back to her seat. “Sorry, sorry,” she says with a meek chuckle. “We still have two predictions to examine,” Ocellus continues. “Now Gallus predicted that he would get a higher score than Yona. Now if that prediction was true, then Gallus would had to have scored an even-numbered score … but it couldn’t be 94, since that was the lowest score. So he either scored 96 or 98, and Yona would have scored 95.” Silverstream picks up where Ocellus leaves off: “But if Gallus had a wrong prediction, then he would had to have scored an odd-numbered score, and lower than Yona. But that means he couldn’t have a 99, so he would have either a 95 or 97, and Yona would have the 99.” “EXCELLENT WORK, SILVERSTREAM!” The students turn to Twilight, who blushes a bit for her outburst. “Sorry … I’ll be quiet from now on,” she states before going silent. “So what about that last prediction?” Sandbar asks. “We can’t get much from that, can we?” “Well, no,” Ocellus admits. “If it’s true, then Silverstream got an even score and I got either the 97, 98, or 99. And if it’s false, then she got an odd score and I got either the 94, 95, or 96. So yes, a lot of possibilities.” “So now what?” Smolder asks. “Now we guess … I guess,” Gallus states. “I’m open to starting with anycreature.” “I say we start with Smolder getting the 96,” Ocellus suggests. “If anyone else got the 96, we’ll know she got the 98.” Sandbar speaks up: “All right … if Smolder got the 96, then … it seems like there’s a lot of ways to assign scores.” “If we then assume my prediction was true,” Gallus says, “then I got the 98 and Yona got the 95.” He ponders a bit further. “Silverstream could then have the 94, and either Sandbar or Ocellus could have the 97 or the 99.” “And if griffin wrong,” Yona adds, “then Yona get 99 and griffin get lower score, like 95. And maybe seapony get 94 again, and Ocellus get 98 and Sandbar 97. That work too, right?” “I could have gotten 97 myself, right?” Silverstream adds. “But that’s the whole point, right?” Ocellus concludes. “Knowing that Smolder got the 96 leads to too many possibilities … so Smolder couldn’t have gotten the 96. She must have gotten the 98, and someone else got the 96.” Upon hearing this comment, Twilight’s horn glows as a quiz paper floats from the desk to Smolder’s seat. The dragon picks up the page. “ALRIGHT, a 98!” she proudly declares. “And now we know one of the six scores,” Sandbar adds. “Where do we go from here?” “I’ll give this a go,” Gallus says. “If I got the 96, then that means Yona got the 95. After that … there’s the 94, 97, and 99 left for Sandbar, Silverstream, and Ocellus. Silverstream could have the 94, and if she did, we still don’t know who got the 97 and who got the 99. So … I guess that means I didn’t get the 96.” “And since griffin not get 98 either,” Yona adds, “that mean griffin wrong and Yona get 99!” Another paper levitates from Twilight’s desk towards the group, landing at Yona’s seat. “YES!!!” she triumphantly declares. Gallus turns to the yak. “Yona, you know I meant nothing personal with my prediction, right?” “All good,” Yona replies with a wide smile. With four scores left to determine, Sandbar is next to speak up. “What if I got the 96? That would leave the 94, 95, and 97 for Gallus, Silverstream, and Ocellus. Then Silverstream could have the 97, and Gallus would have the 95 and Ocellus the 94.” “Sounds good to me!” Silverstream declares. “Wait a minute,” Ocellus counters. “Silverstream could have gotten the 94 instead, and I would have had the 97. So again, there’s no way to know for certain.” “So there’s only two possibilities left for the 96,” Smolder adds. “Right,” Ocellus says as she continues. “Now suppose I got the 96. Then that would mean Silverstream made a false prediction, so she would have either the 95 or the 97, just like Gallus. And Sandbar would have the 94 … only two possibilities, but that’s still one too many. So all that’s left is …” Everyone turns to Silverstream. Seconds pass. “… OH! … Oh, that means I got the 96!” The hippogriff thinks for a few more seconds. “So my prediction is true … so Ocellus got the 97 … and since Gallus didn’t get the 94, he got the 95 and Sandbar got the 94.” “Then that’s it, isn’t it?” Gallus asks. “From highest to lowest, that means Yona got the 99, Smolder the 98, Ocellus the 97, Silverstream the 96, me the 95, and Sandbar the 94.” Twilight nods as the remaining papers fly towards the students, each landing at their appropriate spot. Quickly, the group stomp their appendages in triumph. “Never been so happy to have the lowest score in class,” Sandbar admits. “Great job, everyone!” “Indeed, you’ve all exceeded all expectations,” Twilight adds. “I think after that little exercise, you’ve all earned some time off from homework.”