An eight-digit number contains two 1s, two 2s, two 3s, and two 4s. The 1s are separated by 1 digit, the 2s by 2 digits, the 3s by 3 digits, and the 4s by 4 digits. What is the number?

# Puzzles

# Black and White

By William Anthony Shinkman, 1880. White to mate in two moves.

# The Last Detail

# Black and White

By Jan Kalendovský. White to mate in two moves.

# Late Again

A problem from P.M.H. Kendall and G.M. Thomas’ *Mathematical Puzzles for the Connoisseur*, 1962: A road runs parallel to a railway until it bends to cross it, as shown. A man normally cycles to work along the road at a constant speed of 12 mph, and when he reaches the crossing he’s normally overtaken by a train traveling in the same direction. One day he was 25 minutes late for work and found that the train passed him 6 miles before the crossing. What was the speed of the train?

# Cheryl’s Birthday

This question appeared in the 2015 Singapore and Asian Schools Math Olympiad, a competition for 14-year-old students from Singapore, Thailand, Vietnam, China, and the U.K. (I’ve amended the language a bit):

Albert and Bernard have just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

May | 15 | 16 | 19 | |||

June | 17 | 18 | ||||

July | 14 | 16 | ||||

August | 14 | 15 | 17 |

Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know it either.

Bernard: At first I didn’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

When is Cheryl’s birthday?

Singapore TV presenter Kenneth Kong posted the question online, and it went viral in a matter of days. The competition organizers had intended it to “sift out the better students” and expected that 40 percent of the competitors would find the solution. What is it?

# Patrolling the Palace

A puzzle by James Tanton:

King Tricho lives in a palace in which every room is a triangle:

Before retiring for the night he’d like to inspect it. Is there a path that will let him visit each room once and only once? He can start anywhere.

# Black and White

A pretty problem by August Vorrath. White to mate in two moves.

# Spirits of the Departed

A wine merchant has three sons. When he dies, he leaves them seven barrels that are full of wine, seven that are half-full, and seven that are empty. His will requires that each son receive the same number of full, half-full, and empty barrels. Can this be done?

# Prime Magic

In his 1976 book *100 Numerical Games*, French puzzle maven Pierre Berloquin asks whether it’s possible to construct a magic square using the first nine prime numbers (here counting 1 as prime):

1 2 3 5 7 11 13 17 19

Is it?