Cunning Numbers
Percentages and Fractions
Pointless Geometry
Chances are?
Odd events
100
John starting counting down from 10001 and I starting counting up from 101. At what number will we meet
5051
100
A perfectly cylindrical bottle contains water. Just by looking at the bottle, it is impossible to tell if more than 50% of the bottle is filled up. You have just a sticky pad. How can you tell if the bottle is more than 50% full or less than 50% full.
Make the bottle stand upright. Use sticky pad to mark water level. Now up turn the bottle. If the new water level is above the sticky pad, the water is more than 50% full
100
Two circles of radius 10 each intersect. The distance between the centers of the circles is 15. What is the length of the largest line parallel to the line joining the centers that can be placed within the intersection area?
5
100
I add numbers 1 through 10. Then I randomly pick 2 consecutive numbers (all of these numbers are positive and not greater than 10). The sum of these 2 consecutive numbers is subtracted from the original sum. What is the probability that the result is divisible by 9?
1/9
100
Starting from 1 I add a bunch of consecutive odd numbers. Can I get 1000000000000000002?
No
200
I collect all 8 digit numbers that are made up of only 2s and 1s. What is the difference between the largest and smallest numbers I have collected?
11111111
200
A fraction is of the form X/33. How many values of X can you chose so that the resulting fraction is irreducible and proper?
30 possible choices for X
200
There are 100 different colors. Using color 1, 1 dot is painted. Using color 2, 2 dots are painted and similarly using color 100, 100 dots are painted. You are allowed to erase all dots of a particular color. What maximum color number would your choose so that the remaining number if dots is divisible by 9. In others words, you have to erase the maximum number of dots of the same color so the remaining number of dots is divisible by 9?
Color 91
200
I take a random 3 digit positive number. What are the chances that the number is even, divisible by 9 and 5?
10/900=1/90
200
I am going to call an odd number special if all digits of the number are odd. How many special 3 digit odd numbers are there?
125
300
I count numbers starting from 100 up till 1000. But, if a number contains a '9', I don't count it. When I reach 1000 how many numbers have I actually counted?
What is 648
300
N=(1-(1/2))(1-(1/3))…..(1-(1/100)). What is N as a simple fraction?
1/100
300
15 dots are placed on a circle. Lines are drawn between every pair of dots. If each line were to use a different color, how many colors would you need?
105
300
I roll two fair dice with numbers 1 through 6 on its faces. If the sum of the two numbers that appear is greater than or equal to their the product, I win. What are the chances I win?
13/36
300
For every odd numb I pick, I pick 3 even numbers. After picking 113 odd numbers, I add all the numbers I have with me. Is the sum odd or even?
Odd
400
I write down numbers from 1 till 100 as 1,2,3,4,….,100. John comes in an replaces all my comas with the number 5. How many total number of 5s are now present in the long string of numbers?
118
400
The weight of a melon plus half the weight of the melon is 9 pounds. What is the weight of the melon?
6 pounds
400
10 equidistant parallel lines are drawn. These 10 lines are duplicated and rotated a bit and overlaid on the original 10 parallel lines. How many small parallelograms are formed
81
400
I take numbers from 1 through 50. If I can make two sets of numbers from these 50 numbers so that the sum of numbers in each set are the same, I win. What are the chances I will win?
0
400
I have 20 positive odd numbers with me. The sum of these odd numbers is divisible by 9. If I remove any one number from list, the sum of the remaining 19 numbers is also divisible by 9. What is the smallest possible sum of my 20 positive odd numbers?
3600
500
I multiply all numbers from 1 to 10. What is the largest power of 3 which will divide the product?
3^4 = 81
500
In an auditorium chairs are arranged to give a square formation. Initial all chairs are occupied by all boys from a class. Then, all boys sitting around the perimeter are replaced by all girls from the class. Most girls came quickly to take their seats. There were 30 girls sitting now. Just a few were still empty. What is the minimum possible number of seats that were empty?
2
500
Draw an equilateral triangle. Then join the mid points of its sides to form a smaller equilateral triangle. The mid points of the sides of the new small equilateral triangle are joined to form a smaller equilateral triangle. This small triangle is painted red. What fraction of the original equilateral triangle is painted red?
1/16
500
I starting counting from 23 upwards. John starts counting down from an unknown 3 digit number which he chooses randomly. What are the chances we meet each other on a 3 digit number?
412/900
500
For every odd number I pick, you pick an even number by simply multiplying my odd number. We play this game for some time and we decide to add our collection of numbers. The result was 1234567. Did we make a mistake?
Yes
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