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How does the sequence of numbers continue?

2021-05-23T14:07:55.959Z


A string of numbers begins with two ones, the third number in the sequence is a two. There are two eights in positions 13 and 14. Which number comes after?


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Photo: DER SPIEGEL

Thank you for the many submissions on the puzzle last week!

I randomly generated five winners from the more than 2,300 e-mails: Tim Brietzke from Freiburg, Wolfgang Hintze (Berlin), Frank Hund (Kirrweiler), Jurgen Moll (Paris) and Gabi Roßmeyer (Hamm).

You will each receive a copy of my new puzzle book "Blind Date with Two Strangers".

The solution was 64, by the way. Here you will find two elegant solutions that do not require a calculator.

The new puzzle revolves around numbers.

The first 14 elements of a sequence are given:

1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8, ...

Which number is next?

The 15th number in the sequence is a 7.

1, 1, 2, 3, 5, 8, 4, 3, 7, 1, 8, 9, 8, 8,

7

, ...

The sequence begins like the famous Fibonacci sequence: each number is the sum of its two predecessors.

However, the seventh number ends: There is a 4. If it were a Fibonacci sequence, there would be a 13 (= 5 + 8) and not a 4.

But there is a connection between the 13 and the 4: The 4 is the sum of the digits of the 13. And that is also the solution we are looking for.

The next number in the sequence is always the cross sum of the number you get by adding the last two numbers.

As long as the sum is one-digit, the sum and the checksum are identical and the sequence is identical to that of Fibonacci.

If you missed a puzzle from the past few weeks, here are the ten most recent episodes:

  • The round is in the square

  • The magic number triangle

  • Built on a gap

  • The racing bike clique

  • A king on the run

  • The carpet repair

  • Brand diversity at Swiss Post

  • Is Dieter the thief?

  • One circle, two points

  • Guess the numbers - but clever

Source: spiegel

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