enigmatic puzzle - (4 of 11: Hitori) What is Pyramid Cult's Favorite Fruit?

<sub>Dear PSE users and moderators,
I’m new here in PSE, but I really need your help. There was this person who gave me a black envelope consisting 10+1 pages of puzzles, and also a scribble saying: “Find our favorites and you will be accepted to join our ‘pyramid cult’. Feel free to ask for help from your beloved friends on PSE. They will surely guide you into all the truth.” I’m also a newbie on grid puzzles, so, could you please give me any hint to solve these? It’s getting harder and harder later on..
- athin</sub>

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Rules:

1. Shade cells so no number appears more than once in 3-directions (parallel with one of the board sides).


2. The sides of shaded cells never touch.


3. White cells form a continuous network.

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^{Special thanks to chaotic_iak for testing this puzzle series!}

Answer

Step 1:

Any cell adjacent to two identical cells must be unshaded (since one of those two must be shaded). The 3 on the middle right should also be unshaded because of the two 14s above it, and the cells just inwards from the corners must also be unshaded (to not block off the corners).

Step 2:

Some trivial deductions: from the 13 on the right, we block out the two other 13s in that row. This gives more unshaded cells, including a 3 which lets us shade the 3 one row lower. (Also, the 5 in the bottom left forces a shaded 5 above and left of it, and the 13 in the bottom left forces a shaded 13 in the bottom middle.)

Step 3:

The 7 with the "a" near the bottom left corner cannot be shaded, because then the two 8s there would be unshaded.
If the 4 in the bottom middle is shaded, then the 8 just below it must be unshaded, and you must also shade the 8s in the middle left and bottom right. Then one of the two 6s near the 4 will break connectivity. So that 4 is unshaded: this then shades the 1 in the top left, then the 10 in the bottom right, then the 8 in the bottom middle and bottom left.

Step 4:

Continuing from that, the 2 in the top left must be unshaded (giving two more shaded 2s), then connectivity resolves the two 7s in the upper middle, then the 14 in the upper right.

Step 5:

If the 9 in the middle is shaded, the two 15s above it must both be unshaded. So the 9 is unshaded, and with a bit more bouncing around, this resolves the rest of the grid:

The shaded cells cover the letters CHIKOO, which is a type of fruit.