Logic Puzzles
Irrational Answers(For answers that are literally irrational or don't make sense)
Triple Digits
Sequences
Oddities
100
One and a half Brandons create one and a half math problems in a day and a half. How many problems can Brandon create in a day?
2/3 of a problem
100
i101
i
100
On an online payment service PayBuddy, there is a 1$ fixed fee for making a payment. Sophia sends x amount of money to her friend Julia and Julia sends four times as much money as Sophia sends. Julia finds she has to pay 3.99 times the amount of money as Sophia after factoring in the 1$ fixed fee. How much money did Sophia send to her friend in dollars?
299
100
What's the sum of 1+2+3+4+...+200?
20100
100
In the addition shown below A, B, C, and D are distinct digits. How many different values are possible for D?
ABBCB
+ BCADA
= DBDDD
7
200
‘There are three doors in front of you. Behind one of the doors is a treasure, but there is nothing behind the other two. After you select a door, someone opens one of the two remaining doors, revealing an empty room. Then, the person offers you the chance to switch to another door. To maximise the probability of choosing the door that hides the treasure, would you switch to another door? Please state the reason behind your decision.
Ask Brandon
200
Name the formula to calculate the volume of a sphere, cylinder, and cone. Also name the area of a equilateral triangle
Brandon knows them all except for equilateral triangles
sqrt3/4 * (side)^2
200
Let n bee a four-digit integer whose digits are all distinct. If 9n, equals the integer obtained by reversing the digits of n, compute n.
1089
200
What's the sum of 1+1/3+1/9+1/27+1/81+......
3/2
200
Find the units digit of 3^88 * 7^87
3
300
‘There are two numbers, each between 1 and 20. The sum of the two numbers is given to Person A, and the product of the two numbers is given to Person B. Person A told Person B that he didn’t know what the two numbers were, and Person B said that he didn’t know either. With that, Person A said that he knew the answer now, and Person B replied that he knew the answer too.
‘What are the two numbers?'
(2,2)
300
A circle of radius 2 is centered at A. An equilateral triangle with side 4 has a vertex at A. What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?
4pi-4sqrt3
300
Brandon is excited to learn he's being paid triple digits in his new job at a fertilizer processing plant! But first, he's got to solve a logistical problem. If in one hour 6 infinitely-regenerated cows "produce" 5 cuts of ribeye, 13 cuts of ribeye produce 7 kgs of candida mold, 2 kgs of candida mold feed 42 cats, and 4 cats produce 1g of high-quality fertilizer. How long, in hours, will it take to 1 immortal and indestructible cow to produce 1 kg of high-quality fertilizer? I'm sorry.
20800/49
300
Given that 1 and 2 yield 9, 3 and 4 yield 20, and 5 and 6 yield 12, find the number after 17 and 12.
Brandon hopefully remembers
300
Danica drove her new car on a trip for a whole number of hours, averaging 55 miles per hour. At the beginning of the trip, abc miles was displayed on the odometer, where abc is a 3-digit number with a>= 1 and a+b+c <= 7. At the end of the trip, the odometer showed cba miles. What is a^2 + b^2 + c^2?
37
400
There are 100 lockers that line the main hallway of Newark Academy. Every night, the school principal makes sure all the lockers are closed so that there will be an orderly start to the next day. One day, 100 mischievous students decide that they will play a prank.
The students all meet before school starts and line up. The first student then walks down the hallway, and opens every locker. The next student follows by closing every other locker (starting at the second locker). Student 3 then goes to every third locker (starting with the third) and opens it if it’s closed, and closes it if it’s open. Student 4 follows by opening every fourth locker if it’s closed and closing it if it’s open. This goes on and on until Student 100 finally goes to the hundredth locker. When the principal arrives later in the morning, which lockers does she find open?
400
A regular hexagon with sides of length 6 has an isosceles triangle attached to each side. Each of these triangles has two sides of length 8. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid?
36sqrt(21)
400
A random whole number from 1 to 1000, inclusive, is selected. What is the probability that when the number is doubled, the number of digits in the number stays the same? (Express your answer as a common fraction)
89/200
400
1
11
21
1211
111221
312211
Brandon knows the answer
400
Hexadecimal (base-16) numbers are written using numeric digits 0 through 9 as well as the letters A through F to represent 10 through 15. Among the first 1000 positive integers, there are n whose hexadecimal representation contains only numeric digits. What is the sum of the digits of n?
21
500
One day, in a gathering of top scientists, one of them wondered out loud whether there exists an integer that you could exactly double by moving its last digit to its front. For instance, 265 would satisfy this if 526 were its exact double—which it isn’t.
Bob the Builder responded, “Of course there is, but the smallest such number has 18 digits.”
So given Dr. Builder's hint, what is the smallest such number?
105263157894736842.
500
If, 1–1+1–1+1–1 ⋯ = 1/2
and, 1–2+3–4+5–6⋯ = 1/4
What is 1 + 2 + 3 + 4 +5 +.. infinity
-1/12
500
The product (8)(8888..8888), where the second factor has k digits, is an integer whose digits have a sum of 1000. What is k?
991
500
How many non-similar triangles have angles whose degree measures are distinct positive integers in arithmetic progression?
59
500
The domain of the function 
is an interval of length m/n, where m and n are relatively prime positive integers. What is m+n?
271