Arrange 3 Knives to Rest on Tips of Handles/Variant

Problem

Arrange $3$ knives so they can support a drinking glass, while in the space between $3$ other glasses placed on the table, another glass can be placed underneath that first glass.

Solution

From the original solution (for which the author of this page had to use beer bottles instead of his wife's precious glassware):

It can be seen that a bottle can be balanced on the platform formed by the three knife blades, if sufficient care is taken to ensure symmetry.

It is also noted that the three blades are higher off the surface of the table than the tops of the three supporting bottles, and so a further bottle can easily be placed underneath them:

Historical Note

This problem is a slightly more challenging variant on the original Arrange 3 Knives to Rest on Tips of Handles as published by Henry van Etten in his $1624$ work Récréations Mathématiques, and dates from Victorian times.

Sources

• 1992: David Wells: Curious and Interesting Puzzles ... (previous) ... (next): Henry van Etten: $112$