What's All This Then?
What's All This Then?
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From a reader: "I could probably listen to the same song
for five hours, but 'Dancing Queen?!?'" Steve's 238 Miles.
We were going to write a long detailed description of how one might arrive at an answer, how one might crack Da Vinci's Other Code. But lucky for us we didn't have to, reader Jeremiah Morris did a better job than we could ever have hoped to. We're sending him a present for his effort and logical skills.
_ _ _ _ _ _ _ _
This was a fun puzzle -- it took quite a while to determine the correct orientation of everything, but that was the point. If you like those who show their work, you'll get plenty of it from me.
Okay, first we'll lay the ground rules for our shorthand. The
four rules can be shown visually like so:
1) H _ U
2) T _ _ M
3) U _ A
4) O _ X
Leonardo's solution provides two clues to supplement the rules:
a) H _ _ _ M or M _ _ _ H
b) W _ _ M
Leo's clue b) conflicts with rule 2) -- the W and T can't both be
three places to the left of the M. Therefore, Leo tossed rule 2),
which means he kept 1), 3), and 4) since exactly one rule was a
lie. Rules 1) and 3) can be joined, to give us:
1a) H _ U _ A
2a) W _ _ M
3a) O _ X
Now, let's look at clue a). The former alternative, H _ _ _ M, conflicts with 1a). The latter, M _ _ _ H, would join with 1a) and 2a) to give us W _ _ M _ _ _ H _ U _ A needing far more than eight slots. Therefore, the solution is clearly that Leo built a new box.
Hmm, that seems in character with Leo, but not so much for a logic puzzle. We must assume Leo didn't see the box normally. Guess we'll have to re-read the problem. It's like six paragraphs, do we really have to? Oh, alright -- there was something about soap -- ahh, here we go:
"... just as he was recovering the soap from between his toes in the water he saw his arrangement ..."
This can be interpreted in three ways:
Interpretation 1: Leo saw the box through his legs as he was bent
over. The box would be behind him, and it would be flipped
vertically and horizontally. Some of the letters would be upside
down, but "frail, tired" Leo may not have noticed the funny
looking A, T, and U. In this case, Leo's clues for the actual box
c) H_ _ _ W or W_ _ _ H
d) W _ _ M
Clue d) is the same as clue b) in the first case -- flipping W and M in both directions gives us the same result. So, with the same line of reasoning, we toss out rule 2), and end up with a combined rule of W _ _ _ H _ U _ A. So, Leo definitely built a new box!
Interpretation 2: Leo saw the reflection of the box in the water
in front of him. The reflection would flip the box vertically but
not horizontally. Reversing this, the clues would be:
e) H _ _ _ W or W _ _ _ H
f) M _ _ W
That's not quite as helpful as the original version, as we can't
rule anything out immediately. From rule e), we know that either
rule 1) or 3) is out:
H _ _ _ W conflicts with H _ U _ A
W _ _ _ H _ U _ A takes too big of a box.
We don't yet know if H _ U or U _ A is the problem.
Let's rewrite our rules so far and see:
1b) H _ _ _ W or W _ _ _ H
2b) M _ _ W
3b) H _ U or U _ A
4b) T _ _ M
5b) O _ X
2b) and 4b) can be combined:
1c) T _ _ M _ _ W
If we combined 1c) with the latter case of 1b), we'd get
T _ _ M _ _ W _ _ _ H
Too many slots. So, the H must be to the left of the W:
1d) T _ H M _ _ W
2d) H _ U or U _ A
3d) O _ X
Now we're getting somewhere - rule 1d) is pretty filled out. There aren't many places for the O _ X rule to go now. Let's mix it in:
1e) O T X H M _ _ W or T _ H M _ O W X
2e) H _ U or U _ A
Neither alternative of 1e) has room to place U _ A, so it's out. That means rule 3) was the lie in Leo's solution. However, we can implement H _ U in either case, so we get:
O T X H M U A W or T A H M U O W X
A double solution?!? Both answers fulfill rules 1), 2), 4), and Leo's two clues as I read them in the reflection case. But there's still one interpretation to go.
Interpretation 3: The box was behind Leo, and he saw it reflected in the water behind his feet. In this case, the box would remain upright, but it would be flipped horizontally. This sounds more promising -- all eight letters can be reflected horizontally without a problem, so we don't need Leo ignoring bad letters. Leo wouldn't notice so much that it's backwards -- after all, the left-handed Leonardo did all his writing that way, so any reversal of the "intricately engraved" letters wouldn't be a big deal.
With the box reflected in this manner, the clues become:
g) H _ _ _ M or M _ _ _ H
h) M _ _ W
We still have to throw out either rule 1) or 3), just as in
Interpretation 2. Combining the clues with the rules, we get the
1f) T _ _ M _ _ W H or H T _ _ M _ _ W
2f) H _ U or U _ A
3f) O _ X
The cases of 1f) and 2f) can be combined in only two ways,
so we can narrow it down again:
1g) T _ U M A _ W H or H T U _ M _ _ W
2g) O _ X
The first case of 1g) doesn't allow for 2g), so we keep the
H T U O M X A W
Those letters were in the box, so Leo saw "WAXMOUTH" in the water at his feet. This, of course, meant nothing to him -- why would even a learned Italian bother to know English back in the 15th century? That was still Middle English, so even a native would be writing "A Mouthe Made off Waxxe" or some such, back when natural resources like E's were more plentiful than today.
Jayson Makar had the correct answer too but he chose to show us it in a slightly different fashion. We'll post the winners names shortly.
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