<ol>
<li><p>40 people are sitting around a table. Everyone noticed that one of the people sitting beside him is wearing a dress of the same colour as him, but the other one was wearing a dress of different colour. What is the number of different dress colours of those people?</p></li>
<li><p>1,10,11,100,101.......What is the next term in the sequence?</p></li>
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<p>Tell me how you figured it out. Thanks in advance :)</p>
<ol>
<li> 2 different colors, look at this example:</li>
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<p>GRRGGRRGGRR…</p>
<p>Notice that each person sits next to a G and a R. Also, the last entry must be G because it is a circle and the first person must sit next to someone of their color!</p>
<ol>
<li> 110</li>
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<p>This sequence is the binary numbers. I don’t know if you are familiar with different bases, but basically, every number is only represented with 0s and 1s instead of digits 1-9. In this case, the first digit is 1, then, you must add another digit to stay with just 0s and 1s, so it becomes 10. For the next number (3), you can increment the 0 to a 1, so you get 11. Then you need to add another digit. Following this pattern, 110 follows 101.</p>
<p>Good luck!</p>
<p>For #1, 2 is correct but it is not the only answer. We can have AABBCC…TT where A, …, T are arbitrary colors. Any coloring works provided that A is not the same color as B, B is not the same color as C, etc. Basically it is possible for there to be between 2 and 20 colors.</p>
<p>For #2, note that we normally count in base 10. That is, a placeholder always represents a power of 10. For binary, placeholders represent powers of 2. For base 3, placeholders represent powers of 3.</p>
<p>For example,</p>
<p>101 in base 10 = 1<em>(10^2) + 0</em>(10^1) + 1<em>(10^0)
101 in base 2 = 1</em>(2^2) + 0<em>(2^1) + 1</em>(2^0) = 5 in base 10</p>
<p>Next number in the sequence is 110.</p>