What is the missing product in this sequence of equations?

[Greg Bernhardt]

If

7x7=4
11x7=6
13x11=6

Then

27x28=?

 

[marcus]

Originally posted by Robert Zaleski
8

I'm impressed, Zaleski. Explain

 

[marcus]

oops your answer changed from 8 to 6!

I still believe you are right, and understand the problem,
so please explain

 

[Robert Zaleski]

Originally, I posted 8. Here's how I arrived at that number.

The difference between prime number 23 and prime number 19 is 4.
The difference between prime number 29 and 23 is 6. Adding 6+4 you get 10. The number your looking for is 27, which is 2 less than 10 or the number 8. I think the number 6 may be another way of looking at it, i.e., 27-23=4, 29-27=2, 4+2=6.

 

[marcus]

Thanks RZ, I don't understand you but I'm still impressed

this problem has a nice open-ended character----maybe we
will be getting further attempts!

 

[Asimir]

6

it's the amount of 'e's in the number

seven (2 'e's) x seven (2 'e's) = 4
eleven (3 'e's) x seven (2 'e's) = 6
thirteen (2 'e's) x eleven (3 'e's) = 6

twenty-seven (3 'e's) x twenty-eight (2 'e's) = 6

 

[Robert Zaleski]

7x7=4

11x7=6

13x11=6

17x13=6

19x17=6

23x19=10

29x23=8

31x29=



Your subtracting the second number in a top row by the first number in the row below it, i.e., 11-7=4, 13-7=6, 17-11=6, etc.

Therefore, 27x28=8 (27-19=8)

 

[Asimir]

I just noticed, this isn't a brain teaser, it's a Brian teaser.
Too bad I don't know anyone called Brian. =P

 

[brum]

RZ -- i thought of that too, but what you did assumes that each "equation" canNOT be done independently, which doesn't seem right. you should be able to do these equations by themselves.

in other words, the answer you get depends on the previous equations you have used.

look:
7x7=4

11x7=6

13x11=6

17x13=6

19x17=6

23x19=10

[27x28 should come right here, but it gets "skipped over" according to your rules (27x28 does not exist in your scheme)]

29x23=8


i think Asimir gets the point

 

[Robert Zaleski]

Well, we gave it a try Brum. Asimir answer looks like a winner.

 

[Reddhawk]

Perhaps each number in the left side of the equation represents an alternate number


7x7=4 this is really: 2 x 2 = 4 so 7 = 2

11x7=6 if 7 = 2 then 6/2 = 3 so 11 = 3

13x11=6 if 11 = 3 then 6/3 = 2 so 13 = 2



Then

27 x 28 = 48


27 ---> 7 + 7 + 13 which is really 2 + 2 + 2 or 6
28 ---> 7 + 7 + 7 + 7 which is really 2 + 2 + 2 + 2 or 8


And 6 x 8 = 48

So then with the substituted numbers 27 x 28 = 48


Hope I didn't make that too complicated!

 

[Astrophysics]

I'm impressed reddhawk, how come I didn't come to that idea. I don't think I'd need to post anything now.

 

[FZ+]

Maybe x isn't an operator at all, but a variable representing that particular digit.

ie.

7x7 -> 747
11x7 -> 1167
13x11 -> 13611

Then

27x28 -> 27?28

So we can consider these not as equations, but as a sequence of numbers.

Sum digits:

747 -> 18
1167 -> 15
13611 -> 12
so 27?28 -> 9

so 27x28 = -10

 

[Greg Bernhardt]

Hint #1: Think about how the numbers are spelled.

 

[Robert Zaleski]

Each of the numbered words begins with one of three letters, i.e. ,S, E, or T.
I’ve assigned each letter a number as follows:
S=2
E=3
T=2

Twenty Seven x Twenty Eight
...(2x2)...x...(2x3)= 24

 

[dduardo]

Wow, I am surpised no one has got this one. I thought there were a bunch of good answers. Well here my try from left field:

7x7

seven -> sev-en = 2 syllables

so 2 x 2 = 4

e-lev-en = 3 syllables

so 3x2 = 6

thirt-teen = 2 syllables

so 2 x 3 = 6

Finally 27x28

twen-ty sev-en = 4 syllables
twen-ty eight = 3 syllables

4 x 3 = 12

12 is my final answer

 

[Greg Bernhardt]

dduardo gets the point! Good work everyone else though!