Counting Board And Quipu
1) In the following Peruvian counting board, determine how many of each item is represented. Please show all of your calculations along with some kind of explanation of how you got your answer. Note the key at the bottom of the drawing.

2) Draw a quipu with a main cord that has branches (H cords) that show each of the following numbers on them. (You should produce one drawing for this problem with the cord for part a on the left and moving to the right for parts b through d.)
(a) [latex]232[/latex]
(b) [latex]5065[/latex]
(c) [latex]23,451[/latex]
(d) [latex]3002[/latex]
Basic Base Conversions
3) 423 in base 5 to base 10 4) 3044 in base 5 to base 10
5) 387 in base 10 to base 5 6) 2546 in base 10 to base 5
7) 110101 in base 2 to base 10 8) 11010001 in base 2 to base 10
9) 100 in base 10 to base 2 10) 2933 in base 10 to base 2
11) Convert 653 in base 7 to base 10 12) Convert 653 in base 10 to base 7
13) 3412 in base 5 to base 2 14) 10011011 in base 2 to base 5
Mayan Conversions
Convert the following numbers to Mayan notation. Show your calculations used to get your answers.
15) [latex]135[/latex] 16) [latex]234[/latex]
17) [latex]360[/latex] 18) [latex]1,215[/latex]
19) [latex]10,500[/latex] 20) [latex]1,100,000[/latex]
Convert the following Mayan numbers to decimal (base–[latex]10[/latex]) numbers. Show all calculations.
21) |
22) |
23) |
24) |
James Bidwell has suggested that Mayan addition was done by “simply combining bars and dots and carrying to the next higher place.” He goes on to say, “After the combining of dots and bars, the second step is to exchange every five dots for one bar in the same position.” After converting the following base [latex]10[/latex] numbers into vertical Maya notation (in base [latex]20[/latex], of course), perform the indicated addition:
25) [latex]32[/latex] + [latex]11[/latex] 26) [latex]82 + 15[/latex]
27) [latex]35 + 148[/latex] 28) [latex]2412 + 5000[/latex]
29) [latex]450 + 844[/latex] 30) [latex]10,000 + 20,000[/latex]
31) [latex]4,500 + 3,500[/latex] 32) [latex]130,000 + 30,000[/latex]
33) Use the fact that the Mayans had a base-[latex]20[/latex] number system to complete the following multiplication table. The table entries should be in Mayan notation. Remember: Their zero looked like this…. Xerox and then cut out the table below, fill it in, and paste it onto your homework assignment if you do not want to duplicate the table with a ruler.
(To think about but not write up: Bidwell claims that only these entries are needed for “Mayan multiplication.” What does he mean?)