August Mindbenders

Holes Between Holes

From my earlier years I remember my mum’s Marble Mosaic set – a board in the form of a hexagonal grid of small holes to put the marbles on.

Given any two marbles placed on the board, there may or may not be a hole exactly midway between the holes on which those marbles are placed.  What is the maximum number of marbles that you can place such that no two holes with marbles on them have a hole midway between them?

[5x5 Hexagonal marble board]


Belt Running

As a long conveyor belt is moving steadily, Gareth runs at 12.5 miles per hour (relative to the belt) along it.  As soon as he gets to the end, he turns and runs back at the same speed, while the belt is still moving at the same speed in the same direction.

It took Gareth 26% of his total running time to get from the beginning to the end of the conveyor belt.  How fast is the belt moving?


Lost Words

In each line, a three-letter word has been omitted from some longer words.  Each line has its own missing word, which stays the same across the line.  Can you put the words back?  (Example: LET makes tabLET, athLETe, pLEThora)

  1. w___, ch___, ___hem, m___le
  2. ___ep, u___r, bu___l, blu___d
  3. ca___, ___her, i___e, st___um
  4. ___el, ___pot, s___, p___o
  5. t___, ___p, c___p, b___ble


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