Puzzles
Patterns
Gauss Contest
100

3210

1920

081?

7524

? = 6

(3 + 2) x 2 = 10
(1 + 9) x 2 = 20
(0 + 8) x 2 = 16
(7 + 5) x 2 = 24

100

-16, -2, 10, 20, 28, 34, 38 what is the next number

40

100


  1. Betty and Ann are walking around a rectangular park with dimensions 600 m by 400 m, as shown. They both begin at the top left corner of the park and walk at constant but different speeds. Betty walks in a clockwise direction and Ann walks in a counterclockwise direction. Points P,Q,R,S,T divide the bottom edge of the park into six segments of equal length. When Betty and Ann meet for the first time, they are between Q and R. Which of the following could be the ratio of Betty’s speed to Ann’s speed?


5:3 11:4 9:4 12:5 11:6



9:4

200

439457

106??4


What are the ? marks

1, 2

200

34, 55, 89, this is part of which sequence?

Fibonacci Sequence

200

In the six-digit number 1ABCDE, each letter represents a digit. Given that 1ABCDE × 3 = ABCDE1, the value of A + B + C + D + E is


26

300

There were 3 people and 5 caps, 2 white caps and 3 black caps, they were arranged in height order so the tallest could see the medium height and shortest and the medium height could see the shortest's cap. The people were asked to find what colour caps they had on their head, the tallest was not able to figure it out and even the medium height could not though knowing this, the shortest figured it out. How?

Explaination physically

300

32, 243, 1024, 3125 are all what type of numbers?

Powers of 5

300

Given 8 dimes (10 ¢ coins) and 3 quarters (25 ¢ coins), how many different amounts

of money can be created using one or more of the 11 coins?


27

400
Buzz the cop is trying to catch the thief, Buzz can move one step and the thief can move one step at a time on the grid. Buzz the cop is 2 units apart from the they're in the square grid. If Buzz starts and takes the first step and him and the thief alternate turns on taking steps, will Buzz cop catch the thief

No

400

107 98 82 57 21 - What is the next number?

-28

400

Four vertices of a quadrilateral are located at (7, 6), (−5, 1), (−2, −3), and (10, 2). The area of the quadrilateral in square units is


63

500

There are 10 prisoners and each of them have a cap either black or white, there are 5 black caps and 5 white caps. A warden asks the prisoners to Make a strategy and figure out what cap is on their head without looking at others caps. They then stand in a line and tell the warden the cooler of their caps. After making a strategy how many prisoners are saved and how.

Answer 9 at least - Working will be shown

500

What is the formula to get this number pattern

1:4, 2:19, 3:84, 4:259, 5:628

n to the power of 4 + 3

500


  1. Ashley writes out the first 2017 positive integers. She then underlines any of the 2017 integers that is a multiple of 2, and then underlines any of the 2017 integers that is a multiple of 3, and then underlines any of the 2017 integers that is a multiple of 5. Finally, Ashley finds the sum of all the integers which have not been underlined. What is this sum?


542 708

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