Easy problem II

Number Theory Level 1

The word B R I L L I A N T BRILLIANT was written 100 100 times to form a long string " B R I L L I A N T B R I L L I A N T B R I L L I A N T B R I L L I A N T ⋯ B R I L L I A N T " "BRILLIANTBRILLIANTBRILLIANTBRILLIANT \cdots BRILLIANT" First, all letters in the even places of the string were erased. Then, in the string obtained, once again all the letters in the even places were erased, and so on. At the end of these operations, only one letter remained. What is this letter?

L B I R N T

Ossama Ismail by Ossama Ismail , 63, Egypt

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1 solution

Jeremy Galvagni
Sep 21, 2018

The only letter that will always be in an odd position, and therefore never erased, is the very first letter: the B \boxed{\text{B}}

This is a nice trick problem. Had the erased letters been sometimes odd positions it would taken more effort.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Erasing the odd positions will be my next problem. :)

Ossama Ismail - 2 years, 8 months ago

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