million

FIGURE 3 The results of the penny-doubling problem A B 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 65535 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 FIGURE 4 The sum of the penny doubling A B C 1 1 1 2 2 3 3 4 7 4 8 15 5 16 31 6 32 63 7 64 127 8 128 255 9 256 511 10 512 1023

FIGURE 5 The first ten counting numbers raised to powers n n^2 n^3 n^4 n^5 n^6 1 1 1 1 1 1 2 4 8 16 32 64 3 9 27 81 243 729 4 16 64 256 1024 4096 5 25 125 625 3125 15625 6 36 216 1296 7776 46656 7 49 343 2401 16807 117649 8 64 512 4096 32768 262144 9 81 729 6561 59049 531441 10 100 1000 10000 100000 1000000 FIGURE 6 The first few powers of 2, 4, 8, and 16 A B C D 2 4 8 16 4 16 64 256 8 64 512 4096 16 256 4096 65536 32 1024 32768 1048576 64 4096 262144 16777216 128 16384 2097152 256 65536 16777216 512 262144 1024 1048576 2048 4194304 4096 16777216 8192