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Reply To: Puzzles


Regarding #89246

Well done @kford_academy.

Each missing leaf has two sides and carries two pages.
The left and right pages of the open book, even with pages missing, are either left odd and right even, or left even and right odd.
The number of the right hand page is always greater than the number of the left hand page.
Any combination of single digits are out because the missing leaves each have two sides, so the remaining single digit numbers cannot be consecutive.
Looking a one and two digit sequences…
The sequence of 2 and 10 is out because both numbers are even.
The sequence of 3 and 21 is out because both numbers are odd.
Similar for 4, 32; 5, 43; 6, 54; 7, 65; 8, 76; 9, 87.
Any combination of two and two digit sequences is out because the left-hand page number needs to be higher than the right-hand page number.
The sequence 3 and 210 (206 pages, 103 leaves missing) is an obvious candidate, being a combination of odd and even numbers.
As is 54 and 321 (266 pages, 133 leaves missing).
I believe the best solution is 43 and 210 (166 pages, 83 leaves missing).

ANSWER Left page 43. Right page 210. Combined sequence 43210. Difference between pages 167. 166 pages missing, or 83 leaves (pages front and back).

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