[math-fun] A triangular puzzle
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column: +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+ The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.
Eric, should we assume the unstated constraint that no two cells have the same value? On Tue, Jun 23, 2020 at 12:44 PM Éric Angelini <bk263401@skynet.be> wrote:
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+
The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.
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Also don't (trailing?) 0's count? (per first row)
On Jun 23, 2020, at 9:51 AM, Allan Wechsler <acwacw@gmail.com> wrote:
Eric, should we assume the unstated constraint that no two cells have the same value?
On Tue, Jun 23, 2020 at 12:44 PM Éric Angelini <bk263401@skynet.be> wrote:
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+
The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.
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If the goal is to find the smallest sum, and if the digit 0 is ignored (as it is in the first row), then you could change 888 to 800, 777 to 700, 666 to 600, 555 to 500, 444 to 400, 333 to 300, 222 to 200, and 111 to 100. Tom Éric Angelini writes:
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+
The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.
I cannot change 111 into 100 as 111 is in the column of 40 (and the zeros are digits, aren’t they?) à+ É. Catapulté de mon aPhone
Le 23 juin 2020 à 19:37, Tom Karzes <karzes@sonic.net> a écrit :
If the goal is to find the smallest sum, and if the digit 0 is ignored (as it is in the first row), then you could change 888 to 800, 777 to 700, 666 to 600, 555 to 500, 444 to 400, 333 to 300, 222 to 200, and 111 to 100.
Tom
Éric Angelini writes:
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+
The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.
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Oh yes, I see what you say, Tom! You are right, my first row is wrong, sorry! à+ É. Catapulté de mon aPhone
Le 23 juin 2020 à 20:58, Éric Angelini <eric.angelini@skynet.be> a écrit :
I cannot change 111 into 100 as 111 is in the column of 40 (and the zeros are digits, aren’t they?)
à+ É. Catapulté de mon aPhone
Le 23 juin 2020 à 19:37, Tom Karzes <karzes@sonic.net> a écrit :
If the goal is to find the smallest sum, and if the digit 0 is ignored (as it is in the first row), then you could change 888 to 800, 777 to 700, 666 to 600, 555 to 500, 444 to 400, 333 to 300, 222 to 200, and 111 to 100.
Tom
Éric Angelini writes:
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+
The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.
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participants (5)
-
Allan Wechsler -
Marc LeBrun -
Tom Karzes -
Éric Angelini -
Éric Angelini