Appendix II: Answers to puzzles from Part 4
1.
15 + 15 = 30 (30 /2 = 15)
10 + 10 = 20 (20 / 2 = 10)
4 +4 = 8 (8 /2 = 4)
15 + 10 + 8 = 33
2.
9 + 1 = 10 (10 - 1 = 9)
4 + 4 = 8 (8 /2 = 4)
4 + 1 = 5 (5 - 4 = 1)
Blue
= 9
Yellow
= 4
Green
= 1
3.
20 + 20 + 20 = 60 (60 / 3 = 20)
20 + 5 + 5 = 30 (30 - 20 = 10, 10 / 2 = 5)
5 - 2 = 3
1 + 20 + 4
= 25
Tricky symbol alert. In this puzzle, they changed up the flowers a bit to add a layer of depth. Besides arithmetic, you also have to do some counting. I almost missed that when I was doing this one.
The
wrong answer would be
2 + 20 + 5
= 27
4.
Ignore
everything on the left of the equal signs for the moment. (Trust me, it’s quicker
this way.)
Base number = 5
20 – 5 = 15
45 – 20 = 25
80 – 45 = 35
If
you subtract the previous line from the current line, the answer is always 10
more. So…
“?” – 80 = 45. “?” = 125
If
you want to get finicky, that means:
1 = 2.5, 2 = 10, 3 = 22.5, 4 = 40, 5 = 62.5.
Now
you could have worked it another way:
5
/ 2 = 2.5, 20 / 2 = 10, 45 / 2 = 22.5, 80 / 2 = 40…and then what? Without know
what “?” is, you’re stuck. Good luck finding the pattern from just the addends.
It’s possible I’m sure, but who has the patience and hair to pull out to sit
there and do it. Just go with my shortcut.
So, there is also the mathematically correct way to go
about things. This one has gotten quite a bit of chatter on Quora by
economists, computer science engineers, mathematicians, etc. (“I think this is really a stupid question to answer,
but I read somewhere that these small stupid questions makes the difference…”
is not really what I was looking for.) The most concise answer I found was this
(most of the others were arguing about whether 1 = 5). (https://www.quora.com/If-1+1-5-2+2-20-and-3+3-45-then-what-is-the-value-of-4+4)
1 + 1 = 5
1 * 1 + (1 + 1) ^ 2 = 1+4 = 5
2 + 2 = 20
2 * 2 + (2 + 2) ^ 2 = 4+16 = 20
3+3=45
3 * 3 + (3 + 3) ^ 2 = 9 + 36 = 45
4 + 4 = ?
4 * 4 + (4 + 4) ^ 2 = 16 + 64 =
80
But
that is as far as the analysis went. But it gives us enough to proceed.
5
+ 5 = ?
5 * 5 + (5 + 5) ^ 2 = 25+ 100 = 125
We’re
done here.
(But if you want additional laughs, here are a couple
of the other Quora threads:
5.
Base number = 8
4 + 2 + 8 = 14
5 +3 + 14 = 22
6 + 4 + 22 = 32
So
7 + 2 + 32 = 41
The
answer from the previous line gets added to the left side of the equation.
Easy, peasy.
6.
2 * 3 = 6
3 * 4 = 12
4 * 5 = 20
5 * 6 = 30
6 * 7 = 42
7 * 8 = 56
8 * 9 = 72
9 * 10 = 90
“??” = 90
We’re
good up to this point. But here’s the rub. While we are correctly identifying a
pattern, are we sure it’s the only possible one? To answer that question, we
need to know the (unwritten) rule we are supposed to follow. Is the second
factor of each line simply the previous line’s second factor plus one? Or
is the rule that we are simply to take whatever the second factor
is as our next line’s first factor?
2 * 4 = 6
4 * 8 = 12
8 * 1 = 20
1 * 27 = 27
and so on.
Following
the alternate rule, both sets of equations are correct, but the first group
(seemingly) has a pattern, but the second group is (apparently) completely
random (since we don’t know if there is yet another unwritten rule governing
how to choose the second factor). The upshot is, we are confident in our first
answer because we assume we know what’s going on. My question is,
do we ever really know what’s going on? It’s very possible then
that this
puzzle has no answer.
7.
116=68
117=79
8.
2 = 25
3 = 325
4 = 4325
5 = 54325
And
6 would equal 654325 and so on forever. Just keep adding whatever is on the
left to the front of whatever is on the right. Not really elegant because the 1
and the 5 from the first line are just hanging out with nothing to do, but you
do have to give it a little thought.
9.
32 + 13 = 45
45 +15 = 60
60 + 17 = 77
77 + 19 = 96
“?” = 96
All
you need to do is establish the pattern.
10.
Observe
the given pattern:
398
= 964, 118 = 164, 356 = 936, 423 = ???
Observe
the first term of the pattern 398 = 964
Square
the first digit, 3 ^ 2 = 9 and then square the third digit, 8 ^ 2 = 64, so the
number is 964.
Observe
the second term of the pattern 118 = 164
Square
the first digit, 1 ^ 2 = 1 and then square the third digit, 8 ^ 2 = 64, so the
number is 164.
Observe
the third term of the pattern 356 = 936
Square
the first digit, 3 ^ 2 = 9 and then square the third digit, 6 ^ 2 = 36, so the
number is 936.
Now,
consider the number 423
Square
the first digit, 4 ^ 2 = 16 and then square the third digit, 3 ^ 2 = 9, so the
number is 169.
So,
the complete pattern is 398 = 964, 118 = 164, 356 = 936, 423 = 169.
Clear?
The short version is that you square the first and third digits of every number
on the left side and then mash up the answers on the right side.
I
wasn’t really happy with this one. With the first three equations, the answer
was split one digit to two. In the final one, it was two to one. It lacked a
pleasing symmetry, which mathematicians crave.
11.
If
3 cats can kill 3 rats in 3 minutes, that means 1 cat can kill 1 rat in 3
minutes. So, 10 cats, 10 rats, 3 minutes. 100 cats, 100 rats, 3 minutes. 7
cats? 7 rats? 3 minutes.
The puzzle is trying to confuse you by making you think the threes are connected somehow because they are all threes. But they are not.
The puzzle is trying to confuse you by making you think the threes are connected somehow because they are all threes. But they are not.
12.
5+4=32
13.
888 + 88 + 8 + 8 + 8 = 1000
As a bonus though, if you don’t stop at addition, you can make 1,000 using 8 eights a few different ways.
(8(8(8+8)-(8+8)/8))-8
(888-8) + 8×(8+8) – 8
((8×(8+8))-((8+8+8)/8))×8
((8×(8+8))-((88/8)-8))×8
(8888-888)/8
8(8×8+8×8)-8-8-8
14.
The
correct answer is #9.
How
to get there? Well, probably a few ways. Trial and error comes to mind first.
Go down the list two by two and see if any are true. Why two by two? Is this
another Noah’s Ark reference? No, but since the statements all refer to one
another, you can’t examine them individually.
This
one is playing with your mind a little bit, too, because it’s making you find a
true statement about false statements.
15.
6
|
8
|
2
|
6
|
4
|
5
|
2
|
0
|
6
|
7
|
3
|
8
|
7
|
8
|
0
|
This
one took a little bit to crack, but I got there. The trick is not to take the
statements in order. Begin with the 4th one. It lets you know right
off the bat what you can ignore. If 7, 3, and 8 are off the table then the 7
and 8 in the fifth statement are, too, as is the 8 in the first statement.
6
|
2
|
|
6
|
4
|
5
|
2
|
0
|
6
|
0
|
Next,
we know from the fifth statement that one number is correct and since the only
number left is 0, it must also be one of the correct numbers from the third
statement. However, both of those statements say the correct numbers are in the
wrong place. The only place 0 does not appear in the first position. One number
down, two to go.
6
|
2
|
|
6
|
4
|
5
|
2
|
0
|
6
|
0
|
In
the statements about “correct” numbers, it is important to understand that none
of them that only 1 number or only 2 numbers are
correct; they mean that at least 1 number or at least
2 numbers are correct. Since 6 appears in all three statements, it’s a safe bet
that it is one of our numbers, which means 4 and 5 are not. With 4 and 5 gone,
2 is the only other number left. All we need to now is find their proper place.
6
|
2
|
|
6
|
||
2
|
6
|
|
From
the first statement, we know that one number is in the right place and the
second tells us both of them are in the wrong place. Since 0 is in the first
position, 6 cannot be. Therefore 2 must be in the right place, meaning that 6
can only go into the second position.
2
|
||
The
combination is 062.
16.
The
first three are right hands, the last one is a left
hand.
17.
This one bites.
18.
(4 – 2), (4 + 2) = 2, 6 = 26
(8 – 1), (8 + 1) = 7, 9 = 79
(6 – 5), (6 + 5) = 1, 11 = 111
(7 – 3), (7 + 3) = 4, 10 = 410
423 = 410
To
do the second half of the challenge, have to switch gears a bit. And I gotta
admit, it feels a little like cheating.
“?”
= z and “?” = 410
We
have established that z = 410. In order to come up with a different x and y
than 7 and 3, we need to change where the split in 410 is. Instead of 4, 10, it
has to be 41, 0.
x – y = 41
x + y = 0
x = 41/2
y = -41/2
41 - (-41) = 41
41 + (-41) = 0
(41 / 2) + (-41 / 2) = 410
19.
10 + 10 + 10 = 30 (30 / 3 = 10)
10 + 4 + 4 = 18 (18 - 10 = 8, 8 / 2 = 4)
4 - 2 = 2
(1/2 * 2) + 10 + 4 = 1 + 10 + 14 = 15
Did
you catch that? Only one half of a coconut in the last line, where the previous
line has two halves.
20.
x + (x / 2) = 6
Uh…um…Fuck.
I have lost my algebra mojo. Okay I just know that a strawberry is 4 and half a
strawberry is 2. Are we good?
…aaannnd
a peach is 1 1/3 and half a peach is 2/3. A tomato is worth 3 1/3. I just know.
(I mean, I must have done the algebra in my head, but damn if I can spell it
out…)
Oh,
wait. If I just…
2 * (x + (x / 2)) = 2 * 6 = (2 * x) + x = 12…
Ahem.
So.
1 1/3 + 2/3 = 2
2 * 3 1/3 + 3 1/3 = 6 2/3 + 3 1/3 = 10
4 * 1 1/3 * 3 1/3 = 17 7/9
(17.7777777778).
I hope to shit all the answer numbers line up with the puzzle numbers because it has taken me three days just to format this in Blogger from the original Word document; I'm not going back at this point and rechecking everything.
I’m
outta here.
