Colorado Smith and Brunnhilde had battled their way past the pit of giant anacondas, the lake of liquid lava and the tunnel of the flesh-eating piranhabats. Now they faced the final obstacle before the fabulous treasure cave of the lost Inca princesses.
Three stone pillars rose from the ground to the height of a man's shoulders. Beside them was a pile of thick circular slabs.
Smith peered at his father's tattered notebook. "To pass the pillars and enter the cave, place the correct number of slabs on each pillar. The pillars will sink into the ground. But beware, any error leads to the death of a thousand horrors."
"Yeah, yeah," said Brunnhilde, stepping across a booby-trapped mosaic of a rabid jaguar. "So what are the right numbers?"
"The next page has been damaged. Termites, by the look of it."
Brunnhilde brushed away a piranhabat that was about to devour Smith's ear. "You might have spotted that earlier!"
"I can still read some of it. Er… the numbers of slabs, reading from left to right, are the three digits of a prime number."
"Smith, there are dozens of three-digit primes!"
"True. But each digit is larger than the one to its left."
"There are still several possibilities! It could be 127, or 739—"
"Ah, but any two distinct digits, in either order, form a prime. So 127 is no good, because—for instance—21 isn't prime."
Brunnhilde placed her ear to the ground, and paled. "I can hear a war party approaching!"
Which three-digit prime should Smith use?
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The answer
The three-digit prime is 137.
If any two digits must form a prime, that rules out even digits (which are multiples of 2) and 5 (which are multiples of 5). So the only possible digits are 1, 3, 7, and 9. As these must appear in ascending order of size, there are four possibilities: 137, 139, 179, and 379 (all are prime). But 3 and 9 cannot both occur since 39 is not prime; similarly 1 and 9 can't both occur since 91 is not prime. That leaves only 137. Since 13, 17, 31, 37, 71, and 73 are prime, this number satisfies all the conditions.
The winner was Susanne Halicki, Stockport
