Question

When asked how many paintings he had, an art collector once said: "Six-sevenths of my paintings plus 7." How many paintings does he have?

Answer 1

4 11 26 54 101 177 301 508
7 15 28 47 76 124 207
8 13 19 29 48 83
5 6 10 19 35
1 4 9 16
3 5 7
2 2

Answer 2

thank you

Answer 3

The last diagonal going up on a slant with the last 2 rows shows a progression of increasing by "2". If you look at each small triangle, the top 2 corners subtracted equal the term below.

Interestingly, if you pick a polynomial of sufficiently high enough degree, you can make any number be the next. I could show you a a logical progression of the numbers:

1 2 3 4 5 7 6 8 9 10

Notice how 6 and 7 are reversed, but it can be shown that this has order.

Answer 4

what about this one:

When asked how many paintings he had, an art collector once said: "Six-sevenths of my paintings plus 7." How many paintings does he have?

Answer 5

You're welcome.

Answer 6

The gasoline gauge on a van initially read 1/6 full. When 12 gallons were added to the tank, the gauge read 1/2 full. How many more gallons are needed to fill the tank?

Answer 7

The person who posed the question understands the "any number" principle when he asked "most likely"

Answer 8

Going from 1/6 to 1/2 is an addition of 1/3, so 1/3 corresponds to 12 gallons. Whole tank is 36. Half tank is 18 which is what is needed to fill the rest.

Answer 9

x = (6/7)x + 7 -> x = 49

Answer 10

thank you so much for your help!!!

Answer 11

You're quite welcome! And don't forget that number sequences are only "most likely".

Answer 12

Great, thanks!!! :) :) :)