Download Hottentot Arithmetic

I.
Hottentot Arithmetic
Write the following numbers using words.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
232
301
1223
2030
12312
10001
3021
2222
3102
123
Write the following numbers using numerals.
1.
2.
3.
4.
5.
6.
7.
8.
9.
ondred twoty two
twodred threety one
onesand twodred threety three
twodred two
threesand twoty
oneful twodred threety two
twosand twoty
threeful threedred three
threesand twodred
Add the following numbers
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
23+32
123+132
2022+333
2222+1232
333+303
23+32+13+31
11+22+33+21+32
2002+2032
10301+20203
Sum the first twoty two numbers.
Subtract the following numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
32-21
31-23
211-110
312-123
3012-1213
3001-2222
10101-3232
2000-2
3000-333
2222-323
Multiply the following numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
23 x 32
22 x 33
123 x 22
213 x 312
202 x 32
301 x 103
202 x 220
2222 x 11
2001 x 30
333 x 222
II.
Roman Numerals
Add the following numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
XXXVI + XXVII
LXXIII + CLXVII
XLIV + LXVI
XCVIII + CXXXIV
CCCLIX + CLVIII
DCXCIV + DCCXLIX
MCXI + DLV
CDXLIV + CMXCIX
CCCLXXXVIII + CCCLXXXVIII
D + XCIV
Subtract the following numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
XXXVI - XXVII
CCLXXIII - CLXVII
CXLIV - LXVI
DXCVIII - CXXXIV
CCCLIX - CLVIII
MDCXCIV - DCCXLIX
MCXI - DLV
MCDXLIV - CMXCIX
DCCLXXII - CCCLXXXVIII
D – XCIV
Multiply the following numbers.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
XXII * XXXIII
XXV * XXV
XIV * XXXI
XLIV * XXVII
XCIV * XIX
XXIV * XLIX
XC * XLIV
XXXVIII * XXXVIII
CDXCVII * IV
CXI * XXIX
III.
Konisberg Bridge Problems.
1. Can you walk across each bridge once without retracing your steps?
Can you trace the following diagrams without retracing any line? If so, where could you
start and stop?
Can you walk through each door once and no door twice? If so, draw a path you
could take.
IV.
Patterns and Geometry
How many rectangles do you see in the following figures?
How many squares and how many rectangles can you find in the following size grids?
1.
3.
5.
7.
9.
11.
3X4
6X8
9X3
7X7
12 X 4
5X5
2.
4.
6.
8.
10.
12.
4X3
5X7
4X8
8X8
12 X 2
10 X 5
V.
Base Arithmetic
Convert 2451 (base 10) to its equivalent number in the following bases.
1. Base 4
4. Base 8
2. Base 5
5. Base 9
3. Base 7
6. Base 3
Convert the following numbers to their equivalent number in base 10.
(The base of the number is in parentheses.)
1. 4432 (6)
4. 22103 (4)
2. 4432 (8)
5. 22103 (7)
3. 4432 (5)
6. 22103 (9)
Convert the following numbers from the given base to the requested base.
1.
2.
3.
4.
5.
Number
From Base
To Base
2435
2435
3054
12032
12345
7
6
8
4
8
6
7
5
9
4
Perform the following operations in the base indicated.
Base
7
9
8
6
2.
4.
6.
8.
46+73
46+73
364+245
364+354
Base
9
8
7
8
1.
3.
5.
7.
23+45
23+45
234+345
234+345
9.
11.
13.
15.
17.
19.
43-25
43-25
321-123
321-123
321-123
30020-1232
8
6
4
5
8
5
10.
12.
14.
16.
18.
20.
73-46
73-46
642-354
642-354
201-132
3000-202
9
8
9
7
5
4
21.
23.
25.
27.
23x32
243x45
246x354
2041x304
4
6
7
5
22.
24.
26.
28.
23x32
243x45
246x354
2003x3020
5
8
9
4
Optional: Do problems 21-27 using the Galley Method.
VII.
1.
2.
3.
4.
5.
6.
Fibonnaccii Sequence and Rabbit Farms
Write the first 20 numbers of the Fibonnacci Sequence.
What is the largest 3 digit Fibonnacci number?
What is the smallest 4 digit Fibonnacci number?
800 is between what two Fibonnacci numbers?
Of the first fifteen Fibonnacci numbers, how many are odd and how many are even?
Can you see a pattern for odd and even numbers in the Fibonnacci sequence?
7.
If you are given one new born pair of rabbits on January 1, fill out a chart for 13
months (through next January) assuming you sell the rabbits at age:
a) 3 months
b) 4 months
c) 5 months
d) 6 months.
8.
For each of the above four charts answer the following questions:
a) How many pairs did you own on December 1, after you sold your rabbits?
b) How many pairs will you sell on April 1 (the April 1 after your chart stops)?
c) How many pair of two month old rabbits did you own on November 1?
9.
On January 1, you buy 2 pair of rabbits that are three months old and 3 pair that
are one month old. Fill out a chart assuming you sell rabbits at age:
a) 4 months
b) 5 months
10.
For each of the above two charts answer the following questions:
a) How many did you sell on September 1.
b) What will be the first month you sell at least 10 pair of rabbits?
c) What will be the first month you own more than 100 pair, after selling your
rabbits.?
VIII. Credit Cards and Annuities
1. On January 1, you receive a bill from the credit card company for $2000. You pay
$100. The interest charged is 1% per month on the unpaid balance. How much interest
will you be charged during the month of January?
2. Same scenario as above. What will your bill be on February if you do not charge
anything during the month of January?
3. Same scenario as question #1, but the interest charged is 2% per month on the unpaid
balance. How much interest will you be charged during the month of January?
4. On January 1, you receive a bill from your credit card company for $2500. You pay
100 dollars and charge 400 dollars that month. When the bill comes in February, you pay
$75 dollars and charge 300 dollars that month. If the interest rate is 1.5% per month on
the unpaid balance, how much interest were you charged for the months of January and
February?
5. On January 1, you receive a bill from your credit card for $1000. The interest charged
is 2% per month on the unpaid balance. You decide to pay it off by paying 100 dollars
per month and not charging anything.
a) On what month will you make the final payment?
b) What will your total payments have been?
c) How much interest did you pay?
d) What percent of your payments went to interest?
6. On January 1, you receive a bill from your credit card for $1000. The interest charged
is 2% per month on the unpaid balance. You decide to pay it off by paying $25 dollars
per month and not charging anything.
a) What will your bill be the next January 1?
b) Before making that payment, how much will you have paid?
c) How much interest did you pay?
d) What percent of your payments went to interest?
7. On January 1, you receive a bill from your credit card for $1000. The interest charged
is 1.5% per month on the unpaid balance. Every month you pay 100 dollars and you
charge 100 dollars (thinking you are breaking even).
a) What will your bill be the next January 1?
b) Before making that payment, how much will you have paid?
c) How much interest did you pay?
d) What percent of your payments went to interest?
8. On January 1, you receive a bill from your credit card for $1000. The interest charged
is 1.5% per month on the unpaid balance. Every month you pay 100 dollars and you
charge 400 dollars.
a) What will your bill be the next January 1?
b) Before making that payment, how much will you have paid?
c) How much interest did you pay?
d) What percent of your payments went to interest?
9. On January 1, you get a new credit card. It charges 2% per month on the unpaid
balance. Every month you charge $400 and, starting with the bill you receive in
February, you pay $50 dollars to the company.
a) On what month will your interest be more than 50 dollars?
b) What will your bill be on June 1?
c) Before making that payment, how much will you have paid?
d) What percent of those payments went to interest?
10. On January 1, 2010 you inherit $500,000. You invest in so that it earns 8% interest
per year. Starting on January 1, 2011 and every January thereafter you withdraw $60,000
every January 1st.
a) How long will it take to withdraw all your money?
b) At the time you have withdrawn it all, how much total will you have
withdrawn?
c) How much total interest did you earn?
d) In what year did the balance in your account (AFTER withdrawal) go below
$400,000
e) In what year did the balance in the account (AFTER withdrawal) go below
$300,000
11. On January 1, 2010 you inherit $300,000. You invest it so that it earns 6% interest
per year. Starting on January 1, 2011 and every January thereafter you withdraw
$25,000 every January 1st.
a) In what year will your balance go below $250,000 (AFTER withdrawal)?
b) At that point in time, how much will you have withdrawn?
c) How much interest will you have earned at that point in time?
d) In what year will you make your final withdrawal?
e) How much total will you withdraw when your balance is zero?
ANSWERS
I.
Hottentot Arithmetic
1.
3.
5.
7.
9.
Write with words
twodred threety two
onesand twodred twoty three
oneful twosand threedred onety two
threesand twoty one
threesand onedred two
1.
4.
7.
122
202
2020
2.
4.
6.
8.
10.
Write with numerals
2.
231
3.
5.
3020
6.
8.
30303
9.
1233
10232
3200
threedred one
twosand threety
oneful one
twosand twodred twoty two
onedred twoty three
Add
1.
4.
7.
10.
121
10120
311
313
2.
5.
8.
321
1302
10100
3.
6.
9.
3021
231
31110
3.
6.
9.
101
113
2001
3.
6.
9.
10032
32203
120030
Subtract
1.
4.
7.
10.
11
123
203
1233
2.
5.
8.
2
1133
1332
Multiply
1.
4.
7.
10.
2122
200322
111100
221112
2.
5.
8.
2112
13130
31102
II.
Roman Numerals
Add
1.
4.
7.
10.
LXIII
CCXXXII
MDCLXVI
DXCIV
2.
5.
8.
CCXL
DXVII
MCDXLIII
3.
6.
9.
CX
MCDXLIII
DCCLXXVI
3.
6.
9.
LXXVIII
CMXLV
CCCLXXXIV
Subtract
1.
4.
7.
10.
IX
CDLXIV
DLVI
CDVI
2.
5.
8.
CVI
CCI
CDXLV
Multiply
1.
4.
7.
10.
DCCXXVI
MCLXXXVIII
MMMCMLX
MMMCCXIX
2.
5.
8.
IV.
Patterns and Geometry
DCXXV
MDCCLXXXVI
MCDXLIV
3.
6.
9.
CDXXXIV
MCLXXVI
MCMLXXXVIII
How many squares and rectangles can you find?
1.
4.
7.
10.
SQ
20
85
140
35
REC
60
420
784
234
V.
Base Arithmetic
2.
5.
8.
11.
SQ
20
50
204
55
REC
60
270
1296
225
3.
6.
9.
12.
SQ
133
70
110
130
Convert 2451 (base 10) to its equivalent number in the following bases.
1. 212,103
4. 4623
2. 34,301
5. 3323
3. 10,101
6. 10,100,210
Convert the following numbers to their equivalent number in base 10.
(The base of the number is in parentheses.)
1. 1028
4. 659
2. 2330
5. 5540
3. 617
6. 14,664
Convert the following numbers from the given base to the requested base.
1.
2.
3.
4.
5.
4112
1514
22,310
482
1,103,211
REC
756
360
780
825
Perform the operations.
1.
4.
7.
10.
13.
16.
19.
22.
25.
28.
101
141
1023
26
132
255
23,233
1,341
131,403
12,121,120
2.
5.
8.
11.
14.
17.
20.
23.
26.
130
601
740
14
277
176
2,132
21,143
100,636
3.
6.
9.
12.
15.
18.
21.
24.
27.
68
642
16
25
143
14
2,122
13,617
1,141,114
VII.
Fibonnacci Sequence and Rabbit Farms
1.
2.
3.
4.
5.
6.
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765
987
1597
610 and 987
10 odd, 5 even
odd odd even – odd odd even – odd odd even – etc.
VIII. Credit Cards and Annuities.
1.
2.
3.
4.
$19
$1919
$38
$77.42