Mind Games, Appendix II: Answers to puzzles from Part 4

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.

This gets tricky and there could be another answer. Here’s what I came up with.

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:

https://www.quora.com/If-1-5-2-10-3-15-4-20-then-5-2,

https://www.quora.com/If-1-5-2-25-3-325-and-4-4325-what-does-5-equal,

https://www.quora.com/If-1-5-2-15-3-20-4-25-then-what-is-5-equal-to)

5.

Kinda the same, kinda different.

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.

This one is trying to trip you up by leaving out what 7 and 8 equal. Don’t fall for it. Just remember your multiplication tables. (OMG, I hated those. But only because I hated writing. Look at me now…) The secret is to see what the pattern is in the second factor in the multiplication for each successive line.

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.

Trying the skipped line technique again. Every answer is 11 more than the previous one.

116=68

117=79

8.

1 = 5

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.

I confess. This one got me. After a couple of failed attempts, I just hung it up. I’m copying the wording exactly from the answer. (https://brainly.in/question/5282354) But I did add some spaces and commas clarity.

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.

 

Whether we’re looking at 10 or 100, the pathway to the answer is the same. And the answer is the same…

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.

12.

I was tired and just couldn’t do this one. Had I been fresh, who knows. (I still doubt it, because my mind hasn’t processed something like this in a loooong time.

5+4=3²

13.

It must have been a long day/long night. I didn’t work this one out either.

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.

I hope you didn’t give up on this one too quickly. For some reason, this kind of logic problem really appeals to me.

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 4^th 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.

Well it looks like there are three “odd” ones. Which is true. But we’re only supposed to find one. My hint? It has nothing to do with numbers. This is about gauging your visuo-spatial ability. How well can you turn things over in your mind? Give up?

The first three are right hands, the last one is a left hand.

17.

This one bites.

18.

This one is very much like #10.

But it’s a little bit different as well. The plus sign only tells half the story. You need to subtract and add the numbers, and then mash ‘em up.

(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.

More fractions, less info. Let’s get started.

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.

4 + (4 * 1/2) = 4 + 2 = 6

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.

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Go to Part Four: Fun Time and Epilogue