Medium – Page 15 – Puzzle Prime

The Missing Digit

Section: Brain Teasers Category: Mathematics

Difficulty: Medium

The number 2²⁹ has 9 digits, all different. Which digit is missing?

Bonus: Is the number 9991 prime?

SOLUTION

Let the missing digit be m. Every number and the sum of its digits give the same remainder when divided by 9. The number 2²⁹ = 32 * 64⁴ gives remainder 5 when divided by 9, and therefore 9 divides (0 + 1 + 2 + … + 9) – 5 – m = 40 – m. Thus, the missing digit is 4.

Bonus: 9991 = 10000 – 9 = 100² – 32 = (100 – 3)(100 + 3) = 97 * 103. Therefore the number 9991 is not prime.

Unknown Author April 18, 2020

0 Comments

City of Light

Section: Casual Puzzles Category: Maze

Difficulty: Medium

Get from START to END in this watercolor maze, created by Sean Jackson.

SOLUTION

The solution is shown below.

Sean Jackson March 27, 2020

0 Comments

Hidden Objects Piles

Section: Casual Puzzles Category: Hidden Objects

Difficulty: Medium

Can you find the objects which are hidden in the images below?

SOLUTION

The solution is shown below.

Vook March 24, 2020

0 Comments

Flat as a Leaf

Section: Casual Puzzles Category: Riddle

Difficulty: Medium

It is flat as a leaf, round as a ring,
Has two eyes, yet cannot see a thing.

What is it ?

SOLUTION

The answer is BUTTON.

Unknown Author March 15, 2020

6 Comments

WWII Planes

Section: Brain Teasers Category: Lateral

Difficulty: Medium

During World War II, the mathematician Abraham Wald was asked to help with determining which parts of the allied forces’ planes must be armored better. After examining the surviving American planes, he noticed that there were many holes in the fuselage, and very few in the engines. After careful thinking, he suggested that the armor on the engines must be improved. Why?

SOLUTION

Abraham Wald realized that the holes should have been distributed more evenly across the planes. Therefore the planes which had more holes in the fuselage survived, while the planes which had more holes in the engines got destroyed.

Unknown Author March 6, 2020

2 Comments

Truck Too Tall

Section: Brain Teasers Category: Lateral

Difficulty: Medium

A driver needs to pass under a bridge, but his truck is one inch too tall. However, despite this issue, the driver finds a way to continue further. How?

SOLUTION

He deflated slightly the tires of the truck.

Unknown Author February 16, 2020

1 Comment

Cheese Made Backwards

Section: Casual Puzzles Category: Riddle

Difficulty: Medium

Which type of cheese is made backwards?

SOLUTION

The answer is EDAM.

Unknown Author February 13, 2020

5 Comments

Cut the Paper

Section: Brain Teasers Category: Insight

Difficulty: Medium

You have a sheet of paper and a rectangular piece cut from it, as shown in the picture. What is the easiest way to cut the paper into two pieces with equal areas?

SOLUTION

Make a cut through the centers of the small and the big rectangle. The cut will split both the area of the big and the small (absent) rectangle by half, and therefore will do the same to their difference – the given sheet of paper.