Hi, Guest!
Become a Member for an ad-free experience

The Josephus Problem

Josephus Problem (Wikipedia)

I came across a video on this problem yesterday. Cliff had a post on the Josephus Problem on his old blog, but with that page no longer active, I thought it would be fitting to expand on his work.

The Josephus Problem is a fun little mathematical exercise, but this post will be instead exploring the numerology and gematria of the story surrounding the problem, which originates from a story about Jewish soldiers. Historically, gematria has been a predominantly Jewish practice. A big clue is given in the Wikipedia page when they mention the year 1612which is the Jewish gematria of the word JewishThe details of the mechanism used in this feat are rather vague. According to Dowdy and Mays,[3] in 1612 Bachet suggested the specific mechanism of arranging the men in a circle and counting by threes to determine the order of elimination.

"Jewish" = 1612 (Jewish)

In the Jewish Talmud, Baba Kamma 113a says it’s okay to circumvent a non-Jew with subterfuges (lies). A significant amount of words having to do with dishonesty sum to 113. 113 – liE

To illustrate that both English and Jewish/Latin gematria are significant to this riddle, notice how Josephus sums to 113 in one cipher and 1103 in the other:

Josephus = 113 English and 1103 Jewish

The Josephus Problem is about forty-one Jewish soldiers

"Forty-one Jewish soldiers" = 113 (Full Reduction)

The Josephus Problem comes to us from the Siege of Yodfat:The problem is named after Flavius Josephus, a Jewish historian living in the 1st century. According to Josephus' account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave by Roman soldiers.

"The Josephus Problem" = 1163 (English Extended)

"Siege of Yodfat" = 1163 (English Extended)

The Siege took place in Galilee, Judea ProvinceLocation Galilee, Judea Province (modern-day Israel)

"Galilee, Judea Province" = 194 (English Ordinal)

"Josephus Problem" = 194 (English Ordinal)

194 minutes is 3:14 on a clock
3.14 are the first three digits of Pi

"Twenty-two divided by seven" = 314 (English Ordinal)

The smallest equation you can use to get pi is 22÷7
(Alt+227) = π (Pi)
There are 360 degrees in a circle.

"Three hundred sixty" = 227 (English Ordinal)

"The Josephus Problem" = 227 (English Ordinal)

Pi resolves the mathematics of the circle. In the Josephus Problem, 41 soldiers are sitting in a circle

"Circle" = 32 (Full Reduction)

"Josephus" = 32 (Full Reduction)

The Josephus Problem has the same gematria as The circle

"The Josephus Problem" = 83 (Full Reduction)

"The circle" = 83 (English Ordinal)

83 is the 23rd Prime number, syncing up with Flavius Josephus and Jewish soldiers

"Flavius Josephus" = 203 (English Ordinal)

"Jewish soldiers" = 203 (Reverse Ordinal)

Why 41 soldiers? First of all, 41 is the 13th Prime number.

"Josephus" = 103 (Reverse Ordinal)

"Jewish soldiers" = 1030 (English Extended)

With 41 soldiers in the circle, the one who ends up being the last to survive would be soldier #19

Nineteen = 41 Reduction and 130 Reverse

In Jewish gematria, the word nineteen has the same numeric value as the Hebrew word for kill

"Nineteen" = 244 (Jewish)

"להרוג (Kill)" = 244 (Hebrew Gematria)

The 19th Prime number is 67
The Siege of Yodfat was in the year 67 CE

"Jewish soldiers" = 67 (Full Reduction)

There are 19 years in the Moon’s Metonic cycle. The Jewish calendar is lunisolar, observing both Moon phases and revolutions around the Sun. Every 19 years, 7 of them must contain a 13th month.

"Moon" = 197 (Satanic)

Metonic cycle

"Thirteenth month" = 197 (English Ordinal)

Both Sun and Moon and Sun & Moon give us 13‘s in gematria:

"Sun and Moon" = 130 (English Ordinal)"Sun & Moon" = 1300 (Jewish)

The 130th Prime number is 733

"Siege of Yodfat" = 733 (Jewish)

Log In

Lost your password?