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Guest Message by DevFuse

Prof. Templeton

Member Since --
Offline Last Active Oct 14 2013 01:46 AM

Topics I've Started

Major Grumblegutts' Challenge

19 October 2012 - 04:12 PM

Major Grumblegutts stood in his command tent. “I need an exact figure of the number of men this division has available to go against the enemy, not counting those assembled here, of course”, he bellowed.

“Well sir, during the march, as the regular columns passed, I counted that there were five columns more then the number of men in the front line.”, replied one lieutenant.

“Yes, and after they had arrived at camp, I was told that an additional 845 men were added to the front line in order to dig trenches and that four other groups of the same amount were dispatched to other tasks”, said another lieutenant.

“Quite right, and I was in one of those of those groups when I took charge of it, and was given an addition of ten percent from another group to conduct a covert sortie”, offered a sergeant.

“Tell me about this sortie”, commanded Major Grumblegutts, “I understand it did not go well”.

“Well no sir”, the sergeant replied with his eyes downcast. “It did not. I stayed behind in camp to coordinate with the lieutenants. The entire sortie was ambushed and a number of men killed. Of the survivors a sixth managed to make it back to camp. Another eighth of the remaining perished on the enemy’s march back. After arriving at the enemy’s camp another man died of his wounds and a fourth of those remaining attempted to escape the following night, but only two out of three managed to do so and those that didn't were killed as an example. Those that remained were split up into four equal work gangs and sent to separate locations. Two of those gangs were liberated before reaching their destination and have been returned to us, but one in twelve is still not fit for duty”, the sergeant concluded.

Major Grumblegutts furiously scribbled some figures on the back of a discarded slip of paper. “Hhrrumph”, he grunted when finished. “If our intelligence is correct then the enemy has three men to our two, but we have the high ground. This will be a tough fight."

What is the size of the enemy force?

Spoiler for The answer

The tomb of the unknown ruler

17 October 2012 - 05:49 PM

Professor Templeton’s great-great-grandfather, Aloysius Templeton, was a well known explorer and relic collector. One of his collected histories told of a site near Ugarit. There was located an ancient temple and beneath a burial chamber. The identity of the ruler entombed within was lost to the ages until a tome was discovered that shed light on the question. All that was previously known of the long dead leader was that he was one of the three sons of his predecessor, Zimilkar.

The tome had been translated like this:

Zimilkar had three sons, Ammit, Biranu and Canthar. The aged king knew his time was almost due but could not decide among which of his three sons to leave the responsibility of leading the people. He sent each out with many men to mine an equal number of cubic stones of the same size used to construct the city’s central plaza and whoever was first to build a square around the plaza, it also being a square, would be the next ruler.

Biranu returned to the city to find Ammit had gotten there first and was already building a square. A clever man and not one to be outdone by his sibling, Biranu set his men to builduing his square around his brothers. When Canthar returned last and saw what his brothers were doing, he also proceeded to have his square built around Biranu’s.

It happened that all three sons finished their projects on the same day so that when the old king came to inspect he could not tell who had finished first. He noted that both Ammit and Biranu had used all of their stone cubes, but Canthar had four stones left over and on this basis he was disqualified. Among the remaining two sons a contest was devised to determine the successor.

They would have a race upon the central plaza. Biranu, being more athletic and boastful decided to give his brother an advantage. He would allow Ammit to start from the Southern corner of the plaza while he would start from the West and both would finish in the East. Biranu’s path, however, would not be straight. It was to join with Ammit’s path one quarter of the way from the finish along the distance Ammit was to run.

Both men were given the signal to start and they ran as fast as they could. When Biranu reached the point where his path and Ammit’s joined together he saw Ammit was ahead of him by a distance equal to one twentieth of the the total distance Biranu had to cover . It was a well ran race and a close finish.

The rest of the tome is lost to decay, but the winner was still found with the information given and indeed the site of the central plaza was also found by determining the original size and comparing it with the ruins that still remained.

Is the entombed ruler Ammit or Biranu or perhaps neither?

A stroll on the Avenue

16 October 2012 - 07:16 PM

On a warm spring day in 1944, a man strolled from his apartments on the 4th floor of the building he was living in and proceeded up the avenue toward the giant archways at the end. The building he left was near the opposite end of the avenue by the rail station. In the middle of his walk he stopped for a seat beneath a large chestnut tree that lined the wide through-fare (indeed he believed it to be the widest in the city) and pondered the following bit of interesting information. The building he was staying at was on a street with more then twenty addresses but certainly fewer then five hundred and all numbered one, two, three, four, etc from start to finish. The sum of all the addresses from one right up to, and including, his were exactly half of the sum of all the addresses from one up to, and including, the last.

What is the man's name?

Peculiar Bills

15 October 2012 - 09:52 PM

As I sat down to pay some bills this month, a total figure just less than $1500 dollars, I noticed a peculiar relationship. The square root of my mortgage, the electric bill divided by two, the phone bill minus two, the cable bill plus two, the trash collector’s bill times two and the paperboy’s take squared where all the same figure. In even dollars, no cents, of course.

How much were the bills?

Where did all these dowels come from?

03 October 2012 - 04:33 PM

This may have been asked before since it was taken straight from bn’s playbook.

You have an unlimited supply of dowels all of the same length and they can only be connected at their ends. A triangle made by joining three dowels will be a rigid form, but a square made by connecting four dowels can be easily distorted into other shapes without breaking or bending a dowel or disconnecting the ends. As if the end connections were hinged. In three dimensional space the simplest way to brace the square would be to add eight more dowels the form an octahedron.

Attached File  Octahedron.jpg   7.32KB   151 downloads

Let’s assume, however that we are limited to only two dimensions. Without bending, breaking or overlapping dowels, only connecting them at the ends and remaining on a two dimensional plane we can still brace the square by attaching triangles to it. Here is an example with 35 total dowels.
Spoiler for

The question is: What is the fewest number of dowels required to hold a square firm?