The Seven-Dice Shuffle

In a carnival game, you roll seven ordinary dice and then arrange them to form a 7-digit number.

  • If your number is a multiple of 2, you’ll win £2.
  • If your number is a multiple of 3, you’ll win £3.
  • If your number is a multiple of 4, you’ll win £4.
  • If your number is a multiple of 5, you’ll win £5.
  • If your number is a multiple of 6, you’ll win £6.
  • If your number is a multiple of 7, you’ll win £7.

The catch is that you have to announce the prize you’re attempting before you roll the dice. Which prize should you pick?

At first it seems that the £2 prize must be best. If even one of the seven dice produces an even number, you can put that at the end of string and fulfill the condition. This will happen 99.2 percent of the time.

Surprisingly, though, choosing 7 has an even higher success rate, 99.997 percent! “In fact, almost all numbers can be rearranged to make a multiple of 7,” writes James Grime. “But finding the multiple of 7 is the tricky part.” See the paper below for a strategy that will win the jackpot nearly every time.

(James Grime, “The Seven Dice Shuffle,” Recreational Mathematics Magazine 13:22 [June 2026], 95-101.)

| Science & Math

“Humility”

In a certain street are three tailors. The first to set up shop hung out this sign — ‘Here is the best tailor in the town.’ The next put up — ‘Here is the best tailor in the world.’ The third simply had this — ‘Here is the best tailor in this street.’

— John Scott, The Puzzle King, 1899

| Society

Prayer Vigil

A puzzle by F. Nazarov from the May-June 1996 issue of Quantum:

On a certain familiar island, some residents always lie, and the others always tell the truth. The total population is 100. Each resident worships one of three gods, the sun god, the moon god, or the Earth god. One day a visitor asks each resident three questions:

  1. Do you worship the sun god?
  2. Do you worship the moon god?
  3. Do you worship the Earth god?

Sixty residents answer yes to the first question, 40 to the second, and 30 to the third. How many residents are liars?

Click for Answer
| Puzzles

Groundwork

https://commons.wikimedia.org/wiki/File:The_annihilated_civilization.jpg

Like its predecessor, our present civilization may be no more than one of those crops farmers sow to improve their land by the fixation of nitrogen from the air; it may have grown only that, accumulating certain traditions, it may be ploughed into the soil again for better things to follow.

— H.G. Wells, The Outline of History, 1920

| History

Descent

Bycocket is an obsolete word for a kind of cap or headdress. Its entry in the Second Edition of the Oxford English Dictionary contains this woeful note:

Through a remarkable series of blunders and ignorant reproductions of error, this word appears in modern dictionaries as ABACOT. In Hall’s Chron. a bicocket appears to have been misprinted abococket, which was copied by Grafton, altered by Holinshed to abococke, and finally ‘improved’ by Abraham Fleming to abacot (perhaps through an intermediate abacoc); hence it was again copied by Baker, inserted in his Glossarium by Spelman, and thence copied by Phillips, and so handed down through Bailey, Ash, Todd, etc., to 19th century dictionaries (some of which provide a picture of the ‘abacot’), and even inserted in dictionaries of English and foreign languages.

The OED defines abacot as a “variant of bycocket”.

| Language

The Perko Pair

https://commons.wikimedia.org/wiki/File:Ten_onehundredandsixtyone.gif

How many distinct knots have exactly 10 crossings? By the late 20th century, mathematicians believed the number to be 166.

Then, in 1973, New York attorney and part-time mathematician Kenneth A. Perko Jr. discovered that two of these were essentially the same knot.

The correspondence had gone unnoticed for 75 years.

| Science & Math