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MathMagic Cycle 18: Level 4-6 Regular 

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One of the better known works of architecture of the Roman Empire was the
Coliseum. For a few months, at it's maximum splendor (before the senate
began cutting its funding... yes, old problem) there stood an Imperial
Roman Guard in each of its 1000 arches. Imagine the splendor! (Not too
cool if you were the entertainment)

The first budget conscious cut called for the removal of every other 
Imperial Guard. Imagine, one stayed, the next went. The second senate
cut called for the removal of every third guard (from the original count)
So, the order went out that guards of gate 1 and gate 2 (if there was one)
could stay, while guard of gate 3 (and every other third one) had to go...
Naturally, what the senate was doing was getting  rid of some guards, but also 
getting the credit for a lot of "cuts" of gates that had no guard. 

The "cuts" continued number after number, until a diligent member of the
opposition party cried foul. He said " Only some of the cuts are actually
getting rid of guards. A lot of them are not!" Can you build an argument
for this senator? 

Also, if you were a Roman Imperial Guard that every week had to choose a
different gate you had to look after (and run the risk of loosing your
job), which gates would be your choice?


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MathMagic Cycle 18: Level 4-6 Advanced 

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A grandfather clock at my in-laws is known to loose 7 minutes every hour.
On a Sunday, about a month ago I noticed that it was EXACTLY three minutes 
slow- to the second. Later that month, and much to my surprise, the clock 
was EXACTLY at the right time. My father-in-law remarked that he had done
nothing to adjust the clock, and I knew he hadn't. Work with your NTPs to
figure out what day of the week was my second visit (You'll need to figure
the number of days)

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Good luck
MrH