Problems & Puzzles: Puzzles
Puzzle 94. The Domino & the primes
For this puzzle maybe is a good idea you to get a Domino (game).
For the purpose of our questions you can put together the 28 dominoes (pieces) in two type of arrangements:
Arrangement A (just showing 3 pieces):
to produce one number as concatenations of all the numbers
Arrangement B (just showing 3 pieces)
to produce two numbers, one number as a concatenations of all the numbers of the superior row and the other number as a concatenation of all the numbers of the inferior row.
1. Get the largest prime number possible P, using the most of the 28 pieces according to arrangement A, without worrying for any matching between contiguous pieces (as in the normal domino game)
2. Redo the exercise 1 keeping the matching between contiguous pieces as in the normal domino game.
3. Redo exercises 1 & 2 getting the least prime numbers.
4. Get the largest two prime numbers P1 & P2, using the 28 pieces according to the arrangement B, such that (P1-P2) is minimal
5. Redo the exercise 4 getting the least two prime numbers P1 & P2, using the 28 pieces according to the arrangement B, such that (P1-P2) is minimal
Jeff Burch sent (June 4, 2000) the following solution to question 1:
Jeff Heleen, found (16/06/2000) another solution to question 1 but using another version of Domino:
Giuliano Daddario sent (22/8/01)the following solution to question 3.1:
Later (26/8/2001) he sent his solution to the question 3.2:
The Monday 27/8/2001, Giuliano wrote:
666555544663355226600551144443333224400003311110022221, this is the answer to the question 2.
the solution ofpart 4 is:
The solution to the part 5 is:
and their difference is 34455566667777888892.
If Giuliano's solutions are OK, this game is over...