Jewels and potions

In a computer game, you score 7 points for every phial of potion you find and 11 points for every jewel you collect. There is no limit to the number of jewels and phials of potion you can collect.

Some scores are impossible: for instance you can't score 16, but you can score 14 (two phials of potion) or 18 (one phial and one jewel). What scores can you not make?

This is one of many puzzles from the book "Sums for Smart Kids" by Laurie Buxton (published by BEAM education, ISBN 1-903142-22-9), which is available from the publisher (info@beam.co.uk) at £12.50 + £3.53 p&p. In spite of the title, Plus thinks the book will be enjoyed by puzzlers of all ages.

You can send your solution by e-mail to <plus@maths.cam.ac.uk>.

For some challenging mathematical puzzles, see the NRICH puzzles from this month or last month.

If you are stumped by the PLUS issue 14 puzzle, you can see how it's done.