How many integers between 100 and 999, inclusive, have the property th

All three digit multiples of 11 can be written in three different ways except multiples that contain digit 0.

Multiples of 11 with digit 0 can be written in two different ways. eg. 110-101-011. Now 011 is not included between 100 and 999.

100-199:
Multiples: 110, 121, 132, 143, 154, 165, 176, 187, 198.

Note that there is only one multiple with 0.
No of rotations: 8*3 + 1*2= 26.

Now, from 200 to 999, every other group of 100 integers will contain two such multiples containing 0. Eg 209, 220.

No. of rotations per 100 integers in these groups= 7*3 + 2*2 = 25

Total groups: 8
No. of rotations in 800 integers from 200 to 999: 25*8= 200

Total rotations in 900 integers= 26+200= 226

Ans A

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