Some people think a penny does not have much value in today's economy. This puzzle will show you the power of the penny, with a little help from math.
Imagine you are offered several choices in how you can be paid for doing your chores or your part-time job over the next 30 days. Each option includes getting a raise each day.
Which option do you think would make you richest by the end of the month?
Before calculating your potential riches, read and think about the three options. Predict which option you think will be the best.
Will the same option be the best for the whole month? Test your theory by calculating your riches after one week, two weeks, and three weeks. Round to whole pennies.
Option 1
You will receive one penny on the first day. Starting on day two, you will receive twice as many pennies as you did the day before.
- Day 1: You will receive 1 penny.
- Day 2: You will receive 2 pennies.
- Day 3: You will receive 4 pennies.
Option 2
You will receive 10 pennies on the first day. Starting on day two, you will receive an additional 10 more pennies than you did the day before.
- Day 1: You will receive 10 pennies.
- Day 2: You will receive 20 pennies.
- Day 3: You will receive 30 pennies.
Option 3
You will receive 100 pennies on the first day. Starting on day two, you will receive 50% more pennies than you did the day before.
- Day 1: You will receive 100 pennies.
- Day 2: You will receive 150 pennies.
- Day 3: You will receive 225 pennies.
Powerful Pennies Answers
Option 1 (starting with one penny) will make you the richest at the end of 30 days. It will give you a total of $10,737,418.23.
Total Number of Pennies
|
Option |
Week 1 |
Week 2 |
Week 3 |
|
1 |
127 pennies worth $1.27 |
16,383 pennies worth $163.83 |
2,097,151 pennies worth $20,971.51 |
|
2 |
280 pennies worth $2.80 |
1,050 pennies worth $10.50 |
2,310 pennies worth $23.10 |
|
3 |
3,217 pennies worth $32.17 |
58,187 pennies worth $581.87 |
997,378 pennies worth $9,973.78 |
|
Option |
After 30 Days |
|
1 |
1,073,741,823 pennies worth $10,737,418.23 |
|
2 |
4,650 pennies worth $46.50 |
|
3 |
38,350,013 pennies worth $38,500.13 |
Option 1
|
Day |
Pennies Earned |
Total Pennies |
Total Dollars |
|
1 |
1 |
1 |
$0.01 |
|
2 |
2 |
3 |
$0.03 |
|
3 |
4 |
7 |
$0.07 |
|
4 |
8 |
15 |
$0.15 |
|
5 |
16 |
31 |
$0.31 |
|
6 |
32 |
63 |
$0.63 |
|
7 |
64 |
127 |
$1.27 |
|
8 |
128 |
255 |
$2.55 |
|
9 |
256 |
511 |
$5.11 |
|
10 |
512 |
1,023 |
$10.23 |
|
11 |
1,024 |
2,047 |
$20.47 |
|
12 |
2,048 |
4,095 |
$40.95 |
|
13 |
4,096 |
8,191 |
$81.91 |
|
14 |
8,192 |
16,383 |
$163.83 |
|
15 |
16,384 |
32,767 |
$327.67 |
|
16 |
32,768 |
65,535 |
$655.35 |
|
17 |
65,536 |
131,071 |
$1,310.71 |
|
18 |
131,072 |
262,143 |
$2,621.43 |
|
19 |
262,144 |
524,287 |
$5,242.87 |
|
20 |
524,288 |
1,048,575 |
$10,485.75 |
|
21 |
1,048,576 |
2,097,151 |
$20,971.51 |
|
22 |
2,097,152 |
4,194,303 |
$41,943.03 |
|
23 |
4,194,304 |
8,388,607 |
$83,886.07 |
|
24 |
8,388,608 |
16,777,215 |
$167,772.15 |
|
25 |
16,777,216 |
33,554,431 |
$335,544.31 |
|
26 |
33,554,432 |
67,108,863 |
$671,088.63 |
|
27 |
67,108,864 |
134,217,727 |
$1,342,177.27 |
|
28 |
134,217,728 |
268,435,455 |
$2,684,354.55 |
|
29 |
268,435,456 |
536,870,911 |
$5,368,709.11 |
|
30 |
536,870,912 |
1,073,741,823 |
$10,737,418.23 |
Option 2
|
Day |
Pennies Earned |
Total Pennies |
Total Dollars |
|
1 |
10 |
10 |
$0.10 |
|
2 |
20 |
30 |
$0.30 |
|
3 |
30 |
60 |
$0.60 |
|
4 |
40 |
100 |
$1.00 |
|
5 |
50 |
150 |
$1.50 |
|
6 |
60 |
210 |
$2.10 |
|
7 |
70 |
280 |
$2.80 |
|
8 |
80 |
360 |
$3.60 |
|
9 |
90 |
450 |
$4.50 |
|
10 |
100 |
550 |
$5.50 |
|
11 |
110 |
660 |
$6.60 |
|
12 |
120 |
780 |
$7.80 |
|
13 |
130 |
910 |
$9.10 |
|
14 |
140 |
1,050 |
$10.50 |
|
15 |
150 |
1,200 |
$12.00 |
|
16 |
160 |
1,360 |
$13.60 |
|
17 |
170 |
1,530 |
$15.30 |
|
18 |
180 |
1,710 |
$17.10 |
|
19 |
190 |
1,900 |
$19.00 |
|
20 |
200 |
2,100 |
$21.00 |
|
21 |
210 |
2,310 |
$23.10 |
|
22 |
220 |
2,530 |
$25.30 |
|
23 |
230 |
2,760 |
$27.60 |
|
24 |
240 |
3,000 |
$30.00 |
|
25 |
250 |
3,250 |
$32.50 |
|
26 |
260 |
3,510 |
$35.10 |
|
27 |
270 |
3,780 |
$37.80 |
|
28 |
280 |
4,060 |
$40.60 |
|
29 |
290 |
4,350 |
$43.50 |
|
30 |
300 |
4,650 |
$46.50 |
Option 3
|
Day |
Pennies Earned |
Total Pennies |
Total Dollars |
|
1 |
100 |
100 |
$1.00 |
|
2 |
150 |
250 |
$2.50 |
|
3 |
225 |
475 |
$4.75 |
|
4 |
338 |
813 |
$8.13 |
|
5 |
506 |
1,319 |
$13.19 |
|
6 |
759 |
2,078 |
$20.78 |
|
7 |
1,139 |
3,217 |
$32.17 |
|
8 |
1,709 |
4,926 |
$49.26 |
|
9 |
2,563 |
7,489 |
$74.89 |
|
10 |
3,844 |
11,333 |
$113.33 |
|
11 |
5,767 |
17,100 |
$171.00 |
|
12 |
8,650 |
25,750 |
$257.50 |
|
13 |
12,975 |
38,725 |
$387.25 |
|
14 |
19,462 |
58,187 |
$581.87 |
|
15 |
29,193 |
87,380 |
$873.80 |
|
16 |
43,789 |
131,169 |
$1,311.69 |
|
17 |
65,684 |
196,853 |
$1,968.53 |
|
18 |
98,526 |
295,379 |
$2,953.79 |
|
19 |
147,789 |
443,168 |
$4,431.68 |
|
20 |
221,684 |
664,852 |
$6,648.52 |
|
21 |
332,526 |
997,378 |
$9,973.78 |
|
22 |
498,789 |
1,496,167 |
$14,961.67 |
|
23 |
748,183 |
2,244,350 |
$22,443.50 |
|
24 |
1,122,274 |
3,366,624 |
$33,666.24 |
|
25 |
1,683,411 |
5,050,035 |
$50,500.35 |
|
26 |
2,525,117 |
7,575,152 |
$75,751.52 |
|
27 |
3,787,675 |
11,362,827 |
$113,628.27 |
|
28 |
5,681,513 |
17,044,340 |
$170,443.40 |
|
29 |
8,522,269 |
25,566,609 |
$255,666.09 |
|
30 |
12,783,404 |
38,350,013 |
$383,500.13 |