Pennies On A Chessboard
Imagine you have a choice of gifts: $1000.00 or a some pennies on a chessboard. The pennies are arranged on the squares of the chessboard in a pattern. The first square has 1 penny. The second square has 2 pennies. The third square has 4 pennies, etc. Which would you choose?
The table below shows the number of pennies on each square:
That implies a total sum of 1.84 x 1019 pennies or 184,000 trillion dollars!
The table below shows the number of pennies on each square:
| Square | Pennies |
|---|---|
| 1 | 1 |
| 2 | 2 |
| 3 | 4 |
| 4 | 8 |
| 5 | 16 |
| 6 | 32 |
| 7 | 64 |
| 8 | 128 |
| 9 | 256 |
| 10 | 512 |
| 11 | 1024 |
| 12 | 2048 |
| 13 | 4096 |
| 14 | 8192 |
| 15 | 16384 |
| 16 | 32768 |
| 17 | 65536 |
| 18 | 131072 |
| 19 | 262144 |
| 20 | 524288 |
| 21 | 1048576 |
| 22 | 2097152 |
| 23 | 4194304 |
| 24 | 8388608 |
| 25 | 16777216 |
| 26 | 33554432 |
| 27 | 67108864 |
| 28 | 134217728 |
| 29 | 268435456 |
| 30 | 536870912 |
| 31 | 1073741824 |
| 32 | 2147483648 |
| 33 | 4294967296 |
| 34 | 8589934592 |
| 35 | 17179869184 |
| 36 | 34359738368 |
| 37 | 68719476736 |
| 38 | 137438953472 |
| 39 | 274877906944 |
| 40 | 549755813888 |
| 41 | 1099511627776 |
| 42 | 2199023255552 |
| 43 | 4398046511104 |
| 44 | 8796093022208 |
| 45 | 17592186044416 |
| 46 | 35184372088832 |
| 47 | 70368744177664 |
| 48 | 140737488355328 |
| 49 | 281474976710656 |
| 50 | 562949953421312 |
| 51 | 1125899906842624 |
| 52 | 2251799813685248 |
| 53 | 4503599627370496 |
| 54 | 9007199254740992 |
| 55 | 18014398509481984 |
| 56 | 36028797018963968 |
| 57 | 72057594037927936 |
| 58 | 144115188075855872 |
| 59 | 288230376151711744 |
| 60 | 576460752303423488 |
| 61 | 1152921504606846976 |
| 62 | 2305843009213693952 |
| 63 | 4611686018427387904 |
| 64 | 9223372036854775808 |
That implies a total sum of 1.84 x 1019 pennies or 184,000 trillion dollars!
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