# Two IQ Test puzzles nobody knows an answer to [closed]

Well, at least people in my social circles. Nobody's sure what the right answer is to both puzzles. This has been tormenting me for years and I hope somebody here has an idea.

These are the puzzles:

Never mind the highlighted answers (8 and 13). They don't mean anything.

• You really need to charge your battery. – wizzwizz4 Jun 1 '16 at 14:35
• If in the second question the letters stand for digits and words for sum of digits, then there are exactly 3,600 possible solutions of which 840 yield one of the 6 possible answers. For example, (0+6+5+9)-(2+1+7)=3+1+1+5. So forget about this direction. – avnr Jun 1 '16 at 17:30
• OTOH, if in the first "equation" the digits are just digits then there are 13 possible solutions, two of which included the choice of answers: 3467-581=2886 and 5267-931=4336. So forget about this one too. – avnr Jun 1 '16 at 17:39
• Using phone keypad to convert letters to numbers, adding digits results in the given answer for GIRL {20}, but BOY does not convert to one of the given answer options {10, 67,14, 98,2,13}, and the equation does not calculate: G I R L - B O Y = P O O L : 4 4 7 5 - 2 6 9 = 7 6 6 5 : 20 - 17 = 24 Maybe this helps someone? – Chowzen Jun 1 '16 at 19:34

Partial answer with respect to question number 1 (Same answer as Spikee, different reasoning):

( 4 x $\frac{1}{2}$ ) + (9 x 2) = 20
(8 x $\frac{1}{2}$ ) + (5 x 2) = 14
(10 x $\frac{1}{2}$ ) + (3 x 2) = 11

I got nothing yet on Question #2...

Building on @smriti for the second question, I can see two possible answers.

GIRL - BOY = POOR
3467 - 581 = 2886
5267 - 931 = 4336

For both, the sum of the digits in GIRL is 20. The sum of the digits for BOY is either

14 (5+8+1) or 13 (9+3+1),

both of which are possible answers. Based on this duplication, the question is either poorly contrived or summing the digits is not how you get to the values they want.

• Thanks @Wu33o I didn't realize you could format the text that easily. I've always used the <pre> tag to format text in spoilers and it took some fiddling. I just didn't have the time an hour ago to mess with it. – Engineer Toast Jun 1 '16 at 13:25
• Yeah it's nice that you're able to combine formatting. I also usually try some things until it looks the way I want it to look, but I can imagine that you don't want to spend too much time on it :) – Wu33o Jun 1 '16 at 13:31

I think the answer to the first question is:

11

Reasoning

All sequences deal with differences that are divided by 2. 4 + 4 = 8 + 2 = 10 9 - 4 = 5 - 2 = 3 20 - 6 = 14 - 3 = 11

Update

I think the answer to the second question is:

13

Reasoning

Part 1

Exclusion. BOY can't be 10, because then it would be GIRL - BOY = BOY. And that's not correct obviously. It can't be 14 either, because then POOR would have to be 6. If you take the lowest possible numbers (higher than 0), you would get 211?. Where ? is the value for R, which can't be 2 or 1, meaning you get a result higher than the 6 you'd need.

Part 2

Exclusion. The higher values 67 and 98 would mean POOR would be negative. That would mean that if you take the P as the minus (-), you still would need the 3 other letters to contain enough to add up to 78, which is the highest possible difference using 98. Adding up the highest possible values in that case , 998 = 26, doesn't come close to 78. Also, assuming a possitive number, a fictional word of 4 equal letters can only contain 9999, 9+9+9+9 = 36.

Part 3

Exclusion. 2 isn't possible because: Including the use of 0 (zero), you would get BOY = 0 + 1 + ?, where ? can't be 1, so you would not get 2.

Part 4

20 - 13 = 7 POOR = 7 -> 3112 BOY = 13 = 517 GIRL = ? + ? + 2 + ? = 4 + 8 + 2 + 6 This is 'a' solution, which further confirms it should be 13. The actual way of decoding the letters doesn't matter.

For the second question:

If the Letter Is the Letter O set value = 0
Any other letter set value = 5
Sum values
Girl = 5+5+5+5 = 20
Boy = 5+0+5 = 10
Poor = 5+0+0+5 = 10
Girl - Boy = 20-10 = 10 = Poor
Therefore Boy = 10

• If BOY = 10 then GIRL - BOY = BOY not POOR – Juan Carlos Oropeza Jun 1 '16 at 18:58
• @JuanCarlosOropeza If BOY = POOR, then if GIRL - BOY = BOY, then GIRL - BOY = POOR. In this answer, BOY = POOR. I don't think this answer is right, but I don't see the problem you're seeing. – hvd Jun 1 '16 at 22:49
• @hvd 20 - 10 = 10 mean BOY = POOR is like you said 5 = 7 shouldnt have two symbols for same value – Juan Carlos Oropeza Jun 2 '16 at 4:45
• @JuanCarlosOropeza That doesn't make any sense to me. In GIRL = 20 from the question, you already have two ways of writing down the same value, and it's very common to be able to do that, not just in puzzles. – hvd Jun 2 '16 at 5:23

I know the second one:

$\mathrm g=5,\quad\mathrm i=2,\quad\mathrm r=6,\quad\mathrm l=7,\quad\mathrm b=0,\quad\mathrm o=3,\quad\mathrm y=1,\quad\mathrm p=4\\$
This means
\begin{align}\mathrm{girl}&=5+2+6+7=20\\\mathrm{boy}&=0+3+1=4\\\mathrm{poor}&=4+3+3+6=16\\\mathrm{boy}&=\boxed4\end{align}

• The questions are multiple choice and that's not one of the options ;-). – Spikee Jun 1 '16 at 10:44
• oh!! i didn't check the options :>, nvm, i will try again... – smriti Jun 1 '16 at 11:02

Each row is the alphabetical sort of the numbers in English
Only twenty-two is after "three"

Some info on Question #2...

14 or 13
Brute force attack
GIRL - BOY = POOR --> BOY + POOR = GIRL (each letter a unique digit): 78 solutions.
G+I+R+L = 20, then 11 solutions. Two of them has B+O+Y as one of the answers
B:5 G:3 I:4 L:7 O:8 P:2 R:6 Y:1 (B+O+Y = 14) 3467 - 581 = 2886
B:9 G:5 I:2 L:7 O:3 P:4 R:6 Y:1 (B+O+Y = 13) 5267 - 931 = 4336

11

4 / 2 + 9 * 2 = 2 + 18 = 20

8 / 2 + 5 * 2 = 4 + 10 = 14

10 / 2 + 3 * 2 = 5 + 6 = 11

First part from a different angle:

6

Reasoning:

Left two numbers add to 13, right two add to numbers ending in 9 and decrease by 10 going down the columns:
4 + 9 = 13 and 9 + 20 = 29
8 + 5 = 13 and 5 + 14 = 19
10 + 3 = 13 and 3 + 6 = 9

Or another first part possibility:

8

Reasoning:

All the rows add up to a decreasing multiple of 3
4 + 9 + 20 = 33, which = 11 * 3
8 + 5 + 14 = 27, which = 9 * 3
10 + 3 + 8 = 21, which = 7 * 3

I like both the options because they include all three numbers instead of saying the left two equal the right one