## The French Soldier, a hard brain teaser (some math)

Updated list of solvers:

During the 1st World War (1914-1918) a grave was discovered. It belonged to a French soldier who died the last day of a month in another war, in Italy. His halberd lay next to his body. The day carved in the grave’s stone tablet multiplied by the length of the halberd (in feet), multiplied by the half of years between his death and the discovery of his grave, and finally, multiplied by the half of the age of the French commander of the campaign where the soldier died, make 451,066.

Who was the French commander?

*Thanks to Bibao for providing this one; can you figure it out? Will keep a list of solvers above.*

bizarette18| PUZZLE MASTER | Profile June 10th, 2009 - 6:36 pmMy husband says it’s Gaston de Foix, Duc de Nemours. He was 22 when the soldier died in 1512, probably at Brescia, and his grave was found in 1916. I think this is more of a history puzzle than a maths puzzle, but my husband likes military history so he enjoyed it.

Mashplum| PUZZLE MASTER | Profile June 10th, 2009 - 9:26 pmIf the soldier died on Feb. 28, 1525 in the Battle of Pavia, was buried with a 5.493435635123615 foot halberd, and was found in 1916, then his commander was Francis I.

If the length of the halberd has to be a whole number of feet, can you let us know. If it does, I will keep working.

RK| Founder | Profile June 10th, 2009 - 9:35 pmHi there Mashplum- to answer your question about the halberd, ‘yes’.

RK| Founder | Profile June 10th, 2009 - 9:36 pmyour right Bizarette18, this isn’t so much of a math problem, so removed it from the title. Thanks

Mashplum| PUZZLE MASTER | Profile June 10th, 2009 - 10:06 pmI want to change my answer.

If the soldier died on Feb. 29, 1512, was buried with a 7 foot halberd, and was found in 1916, then his commander was Gaston of Foix, Duke of Nemours, age 22.

7 feet is long for a halberd, but I suspect having all whole numbers is best.

joe| Profile June 11th, 2009 - 7:19 amHmmm not sure about the maths, but that French Commander sounds like it may well be Napoleon Bonaparte, with reference to his Italian campaign around 1796 in the French Revolutionary wars.

(I hope I am on the right lines)

tad| Profile June 11th, 2009 - 8:38 amGaston of Foix

7′ Halberd

February 29th 1512 is the date on the grave

Age of commander at the time is 22

The grave was discovered in 1916

29 x 7 x 1/2(1916-1512) x 22/2 = 451,066

(War of the League of Cambrai)

I found the answer with the help of Wikipedia and Excel. I started by looking at how long a Halberd usually is and when they were used most in war. Then I looked at any wars between Italy and France. Using Excel I plugged in all the number ranges I had until i came up with one that fit. I used the year of death as the unknown in the equation, a range of 3-7 feet for the Halberd, 1914-1918 for the year, 28-31 for the date and 20-35 for the age of the commander. There were over a thousand possibilities with these, but only a few came out with a round number for the year. Since the day was the 29th I know it was a leap year, which confirmed the year of 1512. From there a quick Wiki search lead me to the answer of Gaston of Foix.

Great puzzle.

Mashplum| PUZZLE MASTER | Profile June 11th, 2009 - 10:13 amI think is very much a math problem. At least, that is how I approached it.

Undo the two halves by multiplying 451,066 by 4 to get 1,804,264. Factor 1,804,264 to get 2^3 * 7 * 11 * 29 * 101. Since all the numbers have to be integers, and 1,804,264 is not divisible by 30 or 31, the month is February. If you assume the day is the 28th, you are left with 2 * 11 * 29 * 101, none of which is a reasonable length for a halberd. If you make the day the 29th, then you have 2^3 * 7 * 11 * 101 left. 101 must be a factor of the years since the death, as it is too big to be anything else. Halberds would have been in use 404 years prior to WWI (but not likely 202 or 707), giving a date range of 1510 – 1514. 1512 is the only leap year among them. Armed with the year and the names of the two warring nations, it is a simple matter to discover who was known for ordering Frenchmen to poke halberd holes into Italians in 1512 and see if any of them were 22 years old.

All it takes is basic math plus two or three Wikipedia pages. (Granted it took me 3 hours and 2 dozen Wikipedia pages to realize that.)

MFox| Profile June 11th, 2009 - 11:04 amHalberd= 7ft

Date on grave = 29 Feb 1512

Commander Gaston de Foix was 22 years old (and a few months).

Conflict was the War of the League of Cambria.

Gt7| Profile June 11th, 2009 - 1:06 pmNapoleon III, I think…

khelzer| Profile June 12th, 2009 - 11:46 amthe COMMANDER was Napoleon

we don’t know the identity of soldier.

hex| PUZZLE MASTER | Profile June 14th, 2009 - 10:57 amdate of death: D/M/Y with D = 28, 29, 30 or 31

L: length of halberd (~4 to 6 feet)

A: Age of captain (but not specified when as far as I understand)

D x L x ( (1914..1918) – Y) / 2 x A / 2 = 451,066

D x L x ( (1914..1918) – Y) x A = 2 x 2 x 451,066

2 x 2 x 451,066 = 2 x 2 x 29 x 101 x 11 x 2 x 7

Hence D = 28 (impossible to get an acceptable L) or 29

L = 2×2=4 feet assuming L=4 to 6 feet

A can be then 11×2 or 11×7 (both values are improbable). 101 is excluded!

We then assume L=7

A would be logically 2x2x11=44

(1914..1918)-Y=2×101 -> Y = (1914..1918)-202 = 1712..1716

I am inclined to believe that the above value of Y is incorrect

RK| Founder | Profile June 14th, 2009 - 12:00 pmHex- the latter value you assume for ‘L’ is correct

Falwan| Profile June 15th, 2009 - 3:40 amJoseph Jacques Césaire Joffre

hex| PUZZLE MASTER | Profile June 15th, 2009 - 2:25 pmFrankly, I never expected a french military commander age of 22!

Gaston De Foix!

But my analysis above would need to be revised:

if L=2×2=4 feet then the war must have happened in the 13th century, which I trust did not happen then.

Then L must be equal to 7.

A=22

Y=1510..1514

The battle is the battle of Ravenna in 1512. At that time Gaston De Foix was 22. He died in that battle.

Thank you RK for the confirmation about the halberd length

RK| Founder | Profile June 15th, 2009 - 10:02 pmthis one was very hard, not many people got it. Congrats to Bizarette18, Mashplum, Mfox, Hex, Tad

Gt7| Profile June 17th, 2009 - 9:24 am@khelzer

I thought the question was “Who was the French commander?”