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What is the last number? (Posted on 2021-06-14) Difficulty: 1 of 5
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 .

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 1 of 6
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
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