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2

First, solve the first equation Then, the last equation And now to attack the middle equation


2

Here is the answer, along the X and Y axes are the sum of numbers in that row/ column to aid me in the solving process. I do not think any explanation is needed...


4

First thing to notice In the third relation, Option 1 The first relation is Option 2 The second relation is Now the third relation is Final solution


9

I got 6 of them:


3

Here is the solution Reasoning


1

ma is the age of Mark my ist the age of Mindy


2

Let a be Mark and b be Mindy. Then So


1

Assuming that when the final card of the deck is drawn, the running total remains and the deck is reshuffled. The game will continue at most 3 times through the deck. The count begins at zero (0 modulo 3), after the first pass through the deck the sum is ten (1 modulo 3), and after the second it will be twenty (2 modulo 3), and then thirty (0 modulo 3). ...


1

Wrote an R script: install.packages("combinat") require(combinat) #Creates all permutations for drawing four cards data<-permn(1:4) table<-matrix(nrow=length(data),ncol=4) table<-as.data.frame(table) for(i in 1:length(data)){ for(j in 1:4){ table[i,j]<-data[[i]][j] } } #Don't care about Jill's second pull table$V4<-NULL table$sum<-...


3

I'm going to assume that if the fourth card is drawn, and a multiple of 3 is never reached, the game is considered drawn and this is not a win condition for Jack. Let's start with the easy part: Now going through other possibilities: If Jack draws 1: If Jack draws 2: If Jack draws 4: Ultimately, this gives him odds of: EDIT: Adjusting for the fact ...


4

Using the Vinculum: we have:


0

Disclaimer: I'm typing this out as I'm thinking this through, so it's a bit disorganized. I'll go back and work on cleaning this up when I get the time. Initially, looking at the rings: Further testing of these combinations thins this down to: Looking at the rings: Likewise, Now working from Ring E: Finally: Therefore we come to the final solution of:


2

Solution Reasoning


17

We have the following COCA +COLA ----- SODA Next, notice something similar in the Since we have a 4 digit number as the result, we know that But: Thus, Also, we know Thus, the solution is;


13

Based on Omega Krypton's answer,


8

Since we know that Therefore $A$ Hundreds value must carry since $O \neq 0$ Therefore Therefore $O$ We now get And since $S<9$ Then there are many possibilities... any relations I missed out?


7

Full Solution Notation: Deducing $e$ therefore, Deducing $c, f, h$ regarding B, C: only pair available for distance of 4 is: Therefore, Sum of 25 rule renders Deducing the rest regarding A, E: only pair available for distance of 2 is: Therefore, Sum of 25 renders


5

TL;DR Preliminary deductions Left column: Bottom row: In particular, the numbers Option 1 Let's assume Top row: Right column: So we have The remaining numbers are Option 2 Let's assume Top row: Right column: So we have one of the following two possibilities: The remaining numbers are respectively $2,6,8$ or $4,6,8$, so the complete grid is ...


4

Answer Explanation


3

It works with We can rewrite the equation as follows: Clearly this works if which yields the solution stated.


3

Here is one solution. Some observations


4

I have a bad feeling that the answer you’re after is Because This, of course,


1

Maybe I'm missing something but... Reason:


7

I think that in the first case the total sum is Reasoning For the second case


1

The sequence is: Explanation:


3

Here's one that I found: Here is one similar to micsthepick's answer: And here is a hybrid of the two:


1

191, 426, 931, ???, ???, 646, 971, ???, ??? After looking for few minute I found pattern as 1.Sum of digit in series as 11,12,13, ???, ???,16,17,???, ??? 2.the first digit: square of series 1,4,9,1(6),2(5),3(6),4(9),6(4),8(1) 3.the last digit is flipping between 1& 6 So using 1&2&3 pattern :626,591,486,991


5

Complete answer. because


12

Loophole that I discovered: (1) Pretty much based on micsthepick's answer... (2) self-innovated: (3) self-innovated: (4) self-innovated


33

how about this? this is allowed right?


5

I'm not sure if this is allowed, but


4

I believe A, B, P are Some deductions I came to before brute forcing


5

Here's some other words that should get you free ice cream: But why? The answer lies within Words with no two: Words with a two: Now the only question I have is what kind of training the cashiers go through to figure these out.


1

Here is a suggestion for 76:


2

I’m thinking this is wrong, because there are some words that break the pattern, but could it be that So a word that could get you ice cream is I have no idea if this has anything to do with anything, but So could I have a scoop of


2

Here is a suggestion for 86:


6

The answer is Reason: Example:


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