Can you solve it? Succession

Today’s puzzles are about succession, with a lower case ‘s’.

(Apols to readers hoping to find a discussion of the TV series. Although I have made an attempt at making one of the questions relevant.)

First down the runway is Japanese puzzle master Nob Yoshigahara’s masterpiece, one of the most perfect brainteasers of all time.

1. Nob job

What number goes in the circle with the ‘?’?

(No, the 7 in the final circle is not a mistake.)

For the remaining questions, what number comes next in each sequence? Name the successor.

2. Think Roman

0, 0, 0, 0, 4, 9, 5, 1, 1, 0, 55, …

Hint: write out one, two, three, four, five, six, seven, eight, nine, ten, eleven, …and look at the title of this puzzle.

3. Golomb’s sequence.

1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, …

Named after the eminent mathematician Solomon Golomb (whose work inspired the game Tetris), this is an extremely pleasing pattern once you spot it. Hint: think about why are there two 2s and two 3s?

4. The elevator sequence

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, …

Another puzzle is why this sequence got its name.

5. The flagpole sequence

What number comes next, i.e after THIRTEEN?

6. Eban numbers

2, 4, 6, 30, 32, 34, 36, 40, 42, 44, 46, 50, 52, 54, 56, 60, 62, 64, 66…

I’ll be back at 5pm UK with the answers.

PLEASE NO SPOILERS. Instead discuss your favourite sequences, or maybe even your thoughts as to the solution of Succession.

Thanks to the Online Encyclopaedia of Integer Sequences and Eric Angelini for inspiring today’s puzzles.

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

I give school talks about maths and puzzles (online and in person). If your school is interested please get in touch.