## Brainteaser 1542: Precisely what do I mean?

From The Sunday Times, 29th March 1992 [link]

There is a row of 10 boxes and each box contains one object, which is a knife, a fork or a spoon. Each of the three utensils is in at least one box. Here are five true statements to help you answer the questions below:

1. A knife is in more boxes than a spoon is in;
2. A spoon is in more boxes than a fork is in;
3. A knife is not in precisely five boxes;
4. A spoon is not in precisely three boxes;
5. A fork is not in precisely half the number of boxes a spoon is in.

How many boxes contain a knife?

How many boxes contain a spoon?

This puzzle was selected for the book Brainteasers (2002, edited by Victor Bryant), in which it appeared in the following (slightly different) form:

There is a row of ten boxes and each box contains one object, which is a knife, a fork or a spoon. There is at least one of each utensil. Here are five true statements to help you work out how many of each there are:

• A knife is in more boxes than a spoon is in;
• A spoon is in more boxes than a fork is in;
• A knife is not in precisely five boxes;
• A spoon is not in precisely three boxes;
• A fork is not in precisely half the number of boxes a spoon is in.

How many of each utensil are there?

However I think both these formulations are flawed, in that under any reasonable interpretation there are no solutions. In the comments I present a variation that can be solved.

[teaser1542]