Let's start with 1.5 and 1.6.

• Does the method in 1.5 make sense? The procedure is to divide by 2, write down the remainder, then repeat (by dividing now the quotient by 2, writing down the remainder, etc.). The remainders you write down then give the digits in binary (base 2) in reverse order. Try to review this method if necessary in the book.
• The method in 1.6 is somewhat similar, except you're multiplying by 2, writing down the "integer" part and continually multiplying the decimal part by 2. Try to look at the examples in 1.6 as well then.
• Once 1.5 and 1.6 make sense (let us know if you have any other questions), try 1.25 and 1.26. Hint: There's nothing really special about binary (base 2), so think about what might change in the procedures shifting from base 2 to base N.

For 1.29:

• The rules given for base 10 and base 2 are: "A base 10 number is even if and only if it's last digit is even (0, 2, 4, 6, 8)" and "A base 2 number is even if and only if it's last digit is even (i.e. 0)". Try to extend this to a rule that works for base N where N is even.
• The rule given for base 3 is "A base 3 number is even if and only if it has an even number of odd digits". Does this rule still work for other base N where N is odd?

For 1.30:

• Actually 1.30 is an easier version of 1.10 (and is a fairly common "math puzzle/riddle"). As an example of how the "weighing" works, suppose we have weights of 2, 5, and 7. Then we could weigh values of 2, 5, 7 (using single weights), additionally 9 and 12 (using two weights), and 14 (using all three weights).
• The goal of the problem is to be able to weigh anything from 1 to 100 (inclusive).
• Hint 1: We definitely need a weight of 1.
• Hint 2: In the above example I gave, we could weigh 7 using either the 7 gram weight or combining the 2 and 5 gram weights. It is probably NOT efficient to be able to weight something multiple ways.

Hope this helps! Let us know if you have additional questions.