Numberskull

Numberskull is a great new puzzle devised by David Wolstenholme of Topaccolades Limited.

A Numberskull puzzle consists of a grid with 6 = signs and 6 whole number results already on it, together with 9 given whole numbers, all different.  The puzzler simply has to fill in the grid by placing each of the nine numbers into the nine white squares, one in each, and placing any one of the four basic arithmetic operators (+, -, x, ÷) into the grey squares, so that 6 correct equations are formed (3 in left-to-right rows, 3 in top-to-bottom columns).

Numberskull Example

=52
=40
=2
===
 2 3 6 7 11 31 40 44 49
144838

Numberskull Solution

 6 ÷ 2 + 49 = 52 - x ÷ 3 + 44 - 7 = 40 + - + 11 - 40 + 31 = 2 = = = 14 48 38

Note that the first operation is always evaluated first and its result is used in the second operation to produce the overall result.  So, 3 + 4 x 2 means (3 + 4) x 2, which simplifies to 7 x 2 and equals 14.  It does not mean 3 + (4 x 2) which simplifies to 3 + 8 and equals 11.

There is a unique solution. This can be found a step at a time, with no guessing required, by using arithmetic to determine some of the possible ways of achieving the results with the given numbers and, where necessary, by then applying logic to determine more about the positions of the numbers.

Topaccolades also produce Numberskull puzzles in which some of the given numbers and operators are already placed on the grid.  This can make the puzzle easier to solve.

To find out more about Numberskull, including

• techniques for solving the puzzles,
• a fully-worked solution of the above example,
• further examples,
• the software produced to support their generation,
• intellectual property