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From the people behind the Alan Turing Cryptography Competition.
Applications now open for Making Maths at Manchester 2017, a two-day event for year 12 maths students.
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Puzzle 2.

Grobnog the Goblin King is lounging on his Goblin throne, surrounded by 40 of his most trusted lieutenants. They’ve just returned from raiding Lord Valiant’s castle, having stolen a large treasure chest, and Grobnog is distributing its contents to his lieutenants.

"What a haul, my goblins! We’ve not done as well as when we stole Lady Valiant’s dowry and got ourselves over ten thousand gold coins, but we’ve done well for ourselves today!" said Grobnog. "And to show my gratitude, I'll forego my own share of the treasure and distribute it equally to my most trusted goblin lieutenants!"

As his lieutenants heard this, one of them rushed forward to claim his share. "Don’t be greedy, lad!" said Grobnog. He pointed his finger and a fireball was launched at the errant goblin, who promptly exploded. "Never mind him!" said Grobnog, as he distributed the coins amongst his remaining lieutenants. "This won't do," he said, once he had finished. "I’m four coins short to give you all equal shares. I might be a goblin, but I’m fair and I want to make sure you all receive exactly the same amount! Hand the coins back!"

Two goblins were reluctant to give their shares back. Grobnog launched two fireballs at them, exploding them on contact. "Never mind them!" he said to those who were left. "Bring their shares, together with yours, back to me!" Grobnog then counted out the coins again. "This still won't do," he said. "Now there’s one coin left over! Hand the coins back again!"

Some goblins hesitated; they were quite happy with their share and were not keen to give it back. Grobnog grew angry, launching fireballs around his throne room and killing some of his goblin lieutenants indiscriminantly.

"Never mind them!" said Grobnog, as the remaining goblins looked around nervously to see who had survived. "Bring their shares, together with yours, back to me!" Grobnog then counted out the coins again. "Perfect, my goblins," he said. "Now you've all got equal shares and I’ve still got more than half of my trusted lieutenants left alive!"

How many of Grobnog’s trusted lieutentants survived?

Your answer:
No answers can currently be submitted as the competition is closed.
MathsBombe 2017 is organised by the The School of Mathematics at the University of Manchester.
Contact us via mathsbombe@manchester.ac.uk with any queries.