Question

Sir Dwayne is in charge of dragon designs at the King's Toy
Factory. He hopes that his new designs will please the king
*Your Highness," he says. "I have the plans for the toy
dragons. If it pleases you, every 3rd dragon shall billow
clouds of smoke through its nostrils. every 4th dragon shall
breathe fire, every 6th dragon shall have glowing eyes, and
every 8th dragon shall have a tail with spikes on it. i shail
make 100 dragons." The king asks. Sir Dwayne, how many
dragons shall have more than one of these
characteristics?" Sir Dwayne doesn't have the answer. Can
you help him answer the king before he is thrown into the
dungeon?

Answer 1

Answer:

• 24 dragons

Explanation:

Any multiple of 3 and 4 shall blow clouds of smoke through its nostrils and breathe fire. Those are:

• the 12th, the 24th, the 36th, the 48th, the 60th, the 72nd, the 84th, and the 96th dragons.

Hence, that is 8 dragons that shall have both characteristics.

Any multiple of 6 shall have glowing eyes. The common multiples of 6 and 3 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, and 96.

Then, that adds:

• the 6th, 18th, 30th, 42nd, 54th, 66th, 78th, and the 90th dragons:

Hence, add 8 more dragons.

And the common multiples of 6 and 4 are: 12, 24, 36, 48, 60, 72, 84, and 96, all of which are already included.

Any multiple of 8 shall have a tail with spikes on it. Then, you must find the common multiples of 8 and 3, 8 and 4, and 8 and 6.

Common multiples of 8 and 3 are: 24, 48, 72, and 96, which are already included.

Common multiples of 8 and 4 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, and 96. Then, you must add:

• the 8th, the 16th, the 32th, the 40th, the 56th, the 64th, the 80th, and the 88th.

Those are other 8 dragons.

At the end the number of dragons that shall have more than one of these characteristics is:

• 8 + 8 + 8 = 24