1000 non-negative numbers are placed in 1000 boxes.
The sum of every 4 consecutive numbers is 12.
Only first ten and five last are shown below, revealing only 3 numbers.
$0$$$$1$$$ .., .. $2$$$
It is not too difficult to deduct the last number.
This is your task .
Since the sum of every four consecutive numbers is 12, then for any k, if the kth number is n, then the sum of the next three numbers must be (12-n) and so the (k+4)th number must once again be n. In other words the entire string is just a sequence of four numbers repeated over and over.
When k is 1 mod 4, n = 2.
When k is 2 mod 4, n = 0.
When k is 3 mod 4, n = 1.
Thus the last digit, which would be 0 mod 4, is 9.
|
|
Posted by tomarken
on 2021-06-14 08:47:31 |
Solution
