Answer this puzzle.?

Question

Imagine that the digit 7 has been banned from use. So what we would call "the seventh number" is now written using the symbol "8", the eighth number as "9" and the ninth as "10", the tenth is "11", the sixteenth is "18" and so on.
Complete:

The _________ th number is written as 4685.

Answer 1

Angelico B has it right. Without the digit 7, we only have nine digits that we can use to represent all numbers. This means we are now working in base 9. We need to ignore the old meanings of '8' and '9' and remember they now stand for '7' and '8'.

In base nine, the number '10' means "1 nine and zero 1's", and this is the representation for the ninth number. Similarly, the number '100' is really the 81st number; the digits '100' stand for "1 eighty-one, 0 nines and 0 ones." In the same way, if you have four digits, the left-most stands for the number of 729's you have.

Given the number '4685', we compute its value (base 10) as "4 729's plus 6 81's plus 7 nines (yes - SEVEN nines, because the digit 8 is now being used to represent the value 7) plus 5 ones.

That's 4 x 729 + 6 x 81 + 7 * 9 + 5 = 3470.

The 3470th number is written 4685.

If you wanted to do it the hard way, you'd cross out all the numbers containing a '7' from 1 and 4685 and then count the ones left over, OR you could count the ones struck out and subtract from 4685.

The latter method isn't too hard to work out. Start by looking at the numbers from 1 to 100 and strike out all the 7's - that would include 7, 17, 27, 37, 47, 57, 67, 70-79, 87 and 97. Count them up and you've struck 19 numbers out of 100. You would do the same for 200-299, 300-399, and so on. When you got to 700-799, you'd just eliminate all 100 numbers since they begin with a '7'. Continuing upward, you'd eliminate nineteen out of every hundred numbers for the 800's, 900's, 1000's, 1100's and so on up to the 1700's (which would ALL be eliminated). In the same way, the 2700's and 3700's would all be eliminated.

Let's pause when we get to 4600 for a moment; 4600 means we've gone through 46 sets of 100 numbers. Of these, we've struck out 4 complete blocks of 100: 700-799, 1700-1799, 2700-2799 and 3700-3799. Of the remaining 42 sets, we struck 19 numbers from each set, so in total, we've struck 4 x 100 + 42 * 19 = 1198.

Finally, we have to go from 4601 up to 4685. How many numbers do we strike here? 4607, 4617, 4627, 4637, 4647, 4657, 4667 and 4670-4679. That's 17 more numbers struck. Add those to our previous total 1198 and we have struck 1215 numbers...so we just subtract 4685 - 1215 = 3470.

This matches our earlier answer and confirms that both methods work.

Answer 2

3479th

We can count the number of values skipped and subtract that value from 4685 to reach the answer.

100 values: the 3700s
100 values: the 2700s
100 values: the 1700s
100 values: the 700s
10 x 42 values: the nm70s, where nm span 00, 01,...,06,08,...,46
10 x 38 + 6 values: the nmp7s...

Total skipped values skipped =
100+100+100+100+420+386 =
1206

Hence, the (4685-1206)th = 3479th number is written as 4685.
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Alternately, if you recognize this as being a 9-digit base number system, then you can find the value this way:

4685 [base9] = 4x(9^3) + 6x(9^2) + 8x(9^1) + 5x(9^0) [base10]

= 4x729 + 6x81 +8x9 + 5x1 [base10]
= 3479 [base10]

Answer 3

this means that we have a number system with 9 symbols
0, 1, 2, 3, 4, 5, 6, 8 and 9

solution:
5 + 7*9 + 6*9^2 + 4*9^3 = 3470

Answer 4

The 3531th number is written as 4685.

Answer 5

The 3476 th number. will be written as 4685

Answer 6

13 will live. The first boat load will take 5 leaving 4 on shore, 1 to bring the boat back, 4 more get on & to land, 1 brings the boat back and 4 more get in the boat leaving 2 to go down with the ship and onto the shark's buffet.

Answer 7

666 or 667 or 668

Answer 8

4685-591

Answer 9

4684th number
or
4674 th number is written like that because 8 is written nstead of 7

Answer 10

may be the answer is 4695 as 8 is replaced by 9