Boris’s Puzzles

Boris Kordemsky (1907–1999) was born in Kiknur, Kirov Oblast, Russia. He was a mathematician and puzzle creator widely known in Russia for the most popular puzzle book in the Soviet Union, Математическая смекалка or Quick-witted Mathematics which was first published by the Moscow State University in 1954. It was translated into English by Albert Parry and published by Charles Scribner’s Sons, New York, in 1972.

Page 45. Brothers and Sisters
A boy has as many brothers as sisters but each sister has only half as many sisters as brothers. How many brothers and sisters are there in the family?

Puzzle 59. Plus and Minus Signs
This equation has + and - signs missing.
1 2 3 4 5 6 7 8 9 = 100
Here is the only way to insert 7 plus and minus signs between the digits on the left side to make the equation correct:
1 + 2 + 3 -4 + 5 + 6 + 78 + 9 = 100.
Can you do it with only three plus or minus signs? And is there only one solution?

Puzzle 60. The Puzzled Driver
The odometer [display showing distance travelled] of the family car shows 15,951 kilometres. The driver noticed that this number is palindromic: it reads the same backward as forward. “Curious,” the driver said to himself. “It will be a long time before that happens again.” However, only two hours later, the odometer showed a new palindromic number.

How fast was the car travelling in those two hours?

Puzzle 75. The Marker’s Puzzle
In the Soviet machine industry a marker is a man who draws lines on a metal blank. The blank is cut along the lines to produce the desired shape.

A marker was asked to distribute 7 equal-sized sheets of metal among 12 workers, each worker to get the same amount of metal. He could not use the simple solution of dividing each sheet into 12 equal parts, for this would result in too many tiny pieces. What was he to do?

Puzzle 227. A Boating Puzzle
Motorboat M leaves shore A as motorboat N leaves shore B; they move across a lake each at a constant but different speeds. They meet for the first time 500 yards from A. Each returns from the opposite shore without halting, and they meet 300 yards from B.

How long is the lake? Sharp wits can solve the problem with a minimum of calculation. [Boris’s comment]

Puzzle 263. A Shooting Match
Andryusha, Borya, and Volodya each fired 6 shots, and each got 71 points. Andryusha’s first 2 shots got 22 points and Volodya’s first shot got only 3 points. Who hit the bull’s-eye?

Puzzle 279. Three Sages
Three ancient Greek philosophers took a nap under a tree. While they were asleep, a prankster smeared their faces with charcoal. On awakening, they began to laugh, each thinking the other two were laughing at each other. But suddenly one man stopped laughing. How did he realise his own face was also smeared with charcoal?

Answers

❧ There were seven siblings, four brothers and three sisters.

❧ Again, there is only one way: 123 - 45 - 67 + 89 = 100

❧ The first digit of 15,951 could not change in two hours. Therefore, 1 is the first and last digit of the new number. The middle digit would next click on to 0 and the second and fourth digits change to 6. This gives the next palindromic number 16,061. From 15,951 to 16,061 is 110 kilometres in 2 hours. so his average speed was 55 km per hour (35 miles per hour). Obviously a steady driver.

❧ The marker noticed that 7/12 = 1/3 + 1/4, so he cut 4 sheets into 12 thirds, and 3 sheets into 12 fourths. Each worker got one third and one fourth, or 7/12.

❧ At first meeting, the boats have travelled a combined distance equal to the length of the lake; at second meeting, 3 lengths. Since each boat moves at a constant speed, and the time between meetings is equal for both boats, each boat must travel 3 times the distance by the second meeting as the first. Looking at Boat M, it has travelled 500 x 3 = 1,500 yards. Since this is 300 yards longer than the length of the lake, the lake is 1,200 yards long. This calculation may help.

❧ The shots of each of the three men, each adding up to 71 must be:

25, 20, 20, 3, 2, 1
25, 20, 10, 10, 5, 1
50, 10, 5, 3, 2, 1

The first row is Andryusha’s, since it is the only row that contains two numbers whose sum is 22. There are 3s in the first and third row but Andryusha is the first row. The third row must be Volodya’s, and he hit the bull’s-eye.

❧ Person A reasoned: “I can see both the others are smeared but B must be laughing at C because he thinks his own face is not smeared. However if he saw mine was unsmeared as well, he would be surprised at C’s laughing, because C would have no smeared face to laugh at. But B is not surprised so my face is smeared as well as their faces and the joke is on all of us.” So person A stopped laughing.

At August 2026 The Moscow Puzzles book is online at the Internet Archive https://archive.org/details/boris-a.-kordemsky-the-moscow-puzzles-1972/mode/2up