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## 22 December

In bases 3 to 9, the number 112 is: $$11011_3$$, $$1300_4$$, $$422_5$$, $$304_6$$, $$220_7$$, $$160_8$$, and $$134_9$$. In bases 3, 4, 6, 8 and 9, these representations contain no digit 2.
There are two 3-digit numbers that contain no 2 in their representations in all the bases between 3 and 9 (inclusive). Today's number is the smaller of these two numbers.

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