Sequence 1, 3, 7, 12

Which is the next number in the following sequence:

1, 3, 7, 12, 18, 26, 35, 45, 56, ?

This is the so called Hofstadter Figure-Figure Sequence.

The sequence of the differences between the consecutive numbers in the original sequence is 2, 4, 5, 6, 8, 9, 10, 11… These are exactly the natural numbers missing from the original sequence. Therefore, the next number should be 56 + 13 = 69.

Conflicting Words

What unique feature do the following words share?

FRIEND, FEAST, THERE, THOROUGH, FLIGHT, WONDERFUL, RESIGN, ENDURING, PEST, COVERT

Each of these words contains its antonym as a sub-word:

FRIEND – FIEND, FEAST – FAST, THERE – HERE, THOROUGH – ROUGH, FLIGHT – FIGHT, WONDERFUL – WOEFUL, RESIGN – REIGN, ENDURING – ENDING, PEST – PET, COVERT – OVERT

The Car and the Bird

A car weighing 1500kg (including the driver) starts crossing a 20km long bridge. The bridge can support at most 1500kg and, above that weight, it collapses. If halfway through the bridge, a small bird, weighing 200g, lands on the roof of the car, will the bridge collapse?

By the time the car reaches the middle of the bridge, it would have used fuel that weighs more than 200g, so the bridge will not collapse.