*Spoiler for New Scientist Enigma 1757: “Power point” *(Follow the link to see the puzzle.)

The only 3-digit powers of 1-digit numbers are: 128, 256, and 512 (2^7, 2^8=4^4, and 2^9 = 8^3), 243 and 729 (3^5 and 3^=9^3), 125 and 625 (5^3 and 5^4), 216 (6^3), and 343 (7^3).

The four numbers with 2 as the middle digit (125, 128, 625, and 729) can connect to each other but none can connect to anything else, so they’re eliminated, leaving us with the remaining five numbers. Now all we need is the order.

512 can connect only to 216, so if we don’t start with it we have to end with it. But we start with an odd number, so 512 must be the last number and 216 must be second to last.

343 can connect only to 243, so if we don’t end with it we have to start with it. But we end with 512, so 343 must be the first number and 243 must be second.

Then 256 must be in the middle: 343–243–256–216–512.

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