Each installment of the “Science Game” usually begins with solutions to the previous week’s problems and possible discussion; But in this case, due to the summer holidays on the one hand and, on the other hand, some recent difficulties in the comments section, I will limit myself to proposing four puzzles – yes, they are all very interesting and instructive. Many experts:
- I attend a meeting with my partner and there are four couples. When greeting each other, a certain number of handshakes take place. Naturally, no one shakes hands with their partner or shakes hands with the same person more than once. After the greeting phase, I ask everyone there, including my partner, how many hands they have shaken, and the answers I get are all different. How many people did my partner shake hands with?
The author of this neat puzzle is Lars Bertil Ove, all I know is that he’s Swedish (I’d appreciate any info on this from my astute readers).
Determine the truth or falsehood of each of the following statements:
- Only one statement in this list is false.
- Only two and two statements in this list are incorrect.
- Only three and three statements in this list are false.
- Only four and four statements in this list are incorrect.
- Only five and five statements in this list are incorrect.
- Only six and six statements in this list are false.
- Seven and only seven of the statements in this list are false.
- Only eight and eight statements in this list are false.
- Only nine and nine statements in this list are incorrect.
- Ten and only ten statements in this list are incorrect.
In the original version of this issue, in the January 1969 issue, David L. Silverman proposed Journal of Recreational Mathematics, Reports, Commemorating the New Year, 1969; But, for reasons of space, I thought it convenient to reduce them to a dozen.
- On a table, three cards drawn from a deck of pokers arranged face up. To the right of a king are one or two queens. One or two queens to the left of a queen. To the left of a heart are one or two spades. There are one or two bikes to the right of a bike. What cards are those?
This obscure puzzle was created by architect Gerald L. Kaufman’s work. A Book of Modern Puzzles and other logic puzzle books.
Finally, in a collection of “author” puzzles, one from Sam Lloyd, one of the greatest inventors of logic, math and chess puzzles of all time, cannot be missed:
- Imagine that the 4×4 grid in the picture is made up of 40 matches, toothpicks, or other moving parts. At least how many pieces must be removed so that no squares remain? Not only can none of the 16 1×1 squares be left out entirely, but none of the 9 2×2 squares, none of the 4 3×3 squares, and of course, the entire 4×4 square. (Note that the statement of this problem contains a solution to another well-known one: How many squares are there in the picture?).
An interesting and instructive way to approach the problem is to start with simple phases. In the trivial case of a 1×1 square, it is obvious that a toothpick removal is sufficient. And in the case of a 2×2 grid, it is easy to show that 3 toothpicks must be removed to clear all the squares. And in the case of a 3×3 grid…
Considering the prevailing high temperatures, it is recommended not to attempt these puzzles in full sun or during periods of maximum heat.