2.2 KiB
id | title | challengeType | forumTopicId | dashedName |
---|---|---|---|---|
5900f46c1000cf542c50ff7e | Problem 256: Tatami-Free Rooms | 5 | 301904 | problem-256-tatami-free-rooms |
--description--
Tatami are rectangular mats, used to completely cover the floor of a room, without overlap.
Assuming that the only type of available tatami has dimensions 1×2, there are obviously some limitations for the shape and size of the rooms that can be covered.
For this problem, we consider only rectangular rooms with integer dimensions a
, b
and even size s = a \times b
. We use the term 'size' to denote the floor surface area of the room, and — without loss of generality — we add the condition a ≤ b
.
There is one rule to follow when laying out tatami: there must be no points where corners of four different mats meet. For example, consider the two arrangements below for a 4×4 room:
The arrangement on the left is acceptable, whereas the one on the right is not: a red "X" in the middle, marks the point where four tatami meet.
Because of this rule, certain even-sized rooms cannot be covered with tatami: we call them tatami-free rooms. Further, we define T(s)
as the number of tatami-free rooms of size s
.
The smallest tatami-free room has size s = 70
and dimensions 7×10. All the other rooms of size s = 70
can be covered with tatami; they are: 1×70, 2×35 and 5×14. Hence, T(70) = 1
.
Similarly, we can verify that T(1320) = 5
because there are exactly 5 tatami-free rooms of size s = 1320
: 20×66, 22×60, 24×55, 30×44 and 33×40. In fact, s = 1320
is the smallest room-size s
for which T(s) = 5
.
Find the smallest room-size s
for which T(s) = 200
.
--hints--
tatamiFreeRooms()
should return 85765680
.
assert.strictEqual(tatamiFreeRooms(), 85765680);
--seed--
--seed-contents--
function tatamiFreeRooms() {
return true;
}
tatamiFreeRooms();
--solutions--
// solution required