## Five Points, Ten Distances

Five points, A, B, C, D, and E, lie on a line. The distances between them in ascending order are: 2, 5, 6, 8, 9, X, 15, 17, 20, and 22. What is X?

We assume that the points are ordered A to E from left to right. We have AE = 22 and either AD = 20, BE = 17, or AD = 17, BE = 20. Without loss of generality AD = 20, BE = 17, and therefore AB = 5, BD = 15, DE = 2. The distance of 6 is associated with either BC or CD, and therefore the points are arranged in one of these two ways:

1. AB = 5, BC = 6, CD = 9, DE = 2
2. AB = 5, BC = 9, CD = 6, DE = 2

If it is the latter, we get the sequence of distances: 2, 5, 6, 9, 11, 14, 15, 17, 20, 22, which does not fit the provided sequence.

If it is the former, we get the sequence of distances: 2, 5, 6, 8, 9, 14, 15, 17, 20, 22, and therefore X = 14.

## Connect the Squares

Connect the pairs of squares with non-interacting lines that do not cross the black boundary.

A solution is shown below.

## ERGRO

Add the same sequence of three letters both before and after “ERGRO” in order to form an existing English word.

Add the letters U-N-D to get UNDERGROUND.

## 11 is a Racehorse

Can you figure out what story the following sequence of statements is telling?

• 11 is a racehorse
• 12 is 12
• 1111 race
• 12112

11 is a racehorse. 12 is one (1) too (2). 11 won (1) one (1) race. 12 won (1) one (1) too (2).

## Perfect Square Sums

Find all possible arrangements of the numbers 1 to 15 in a sequence, where the sum of any two consecutive numbers is a perfect square.

Note that the number 8 can be neighboring only with the number 1, so it must be at one end of the sequence. The number 15 can be neighboring only with the numbers 1 and 10, so it either needs to be next to 1 or at the other end of the sequence. In either case, 10 should be next to it. The only other number that can be neighboring 10 is 6. Then 3 should follow, then 13 (since 1 is already taken), then 12, then 4, then 5, then 11, then 14, then 2, then 7, then 9. Since 1+9=10 is not a perfect square, we find that the only solutions are

8-1-15-10-6-3-13-12-4-5-11-14-2-7-9

and its reverse.

## Toggle a Pixel

Toggle one pixel to make this equality correct.

(71+1)×(71-1) = 10×9×…×2×1 = 10!

FEATURED

## Eye of the Dragon

Divide the circle below in two pieces. Then, put the pieces together to get a circle with a dragon, such that the dragon’s eye is at the center of the new circle.

The solution is shown below.

## A Horse in Front, A Car Behind

You are sitting on a plane. There is a horse in front of you and a car behind you. Where are you?

You are on a merry-go-round in an amusement park.

## 4-3-2-1

Move one red ball to turn the sequence 1-2-3-4 into 4-3-2-1.

Take the second-to-last ball and place it between the first two balls on the left.

## Cut the Pizza

Cut a circular pizza into 12 congruent slices, such that exactly half of them contain crust.

First, cut the pizza into 6 congruent circular triangles, and then split each of them in half, as shown on the image below.