Take two numbers, such that the square of the first, plus the square of the second, shall equal 8; while the first, plus the product of the first and second, shall equal 6. What are the two numbers?
Jack had only $2, but he needed $3 for his cab fare home. He went to a pawn shop and pawned his $2 for $1.50. Jack then bumped into Don and told him that he would sell him his $2 pawn ticket for $1.50. Dan agreed. Since Jack started out with $2, and he ended up with $3, who is out the extra dollar and why?
A car thief, who had managed to evade the authorities in the past, unknowingly took the automobile that belonged to Detective Anderson. The detective wasted no time and spared no effort in discovering and carefully examining the available clues. He was able to identify four suspects with certainty that one of them was the culprit.
The four make the statements below. From twelve of total statements, six are true and six false.
Suspect A:
1. C and I have met many times before today.
2. B is guilty.
3. The car thief did not know it was the Detective's car.
Suspect B:
1. D did not do it.
2. D's third statement is false.
3. I am innocent.
Suspect C:
1. I have never met A before today.
2. B is not guilty.
3. D knows how to drive.
Suspect D:
1. B's first statement is false.
2. I do not know how to drive.
3. A did it.
Which one is the car thief?
Let's say 6 statements are lies.
A's 1st statement and C's 1st statement negate each other. One of them is a lie.
C's and D's negate each other. One of them is lying. Therefore, there are 4 additional false statements.
Assume A is guilty. If so, A's second statement, B's second statement, and D's first statement are the additional lies.
Assume D is guilty. If so, A's second statement, B's first statement, and D's third statement are lies. This also only makes five false statements. D did not do it.
Assume C did it. If so, A's second statement, D's first and third statements are false. This again, makes only five false statements.
After ruling out suspects A, C and D, B is the culprit. B's third statement, C's second statement, and D's first and third statements are the additional false statements. This adds up to six.
Given two 2s, "plus" can be changed to "times" without changing the results: 2 + 2= 2 x 2.
The solution with three numbers is easy too: 1 + 2 + 3= 1 x 2 x 3.
Now find the answer for 4 numbers and for 5 numbers.
For 4 numbers:
1 + 1 + 2 + 4= 1 x 1 x 2 x 4.
For 5 numbers:
1 + 1 + 1 + 2 + 5= 1 x 1 x 1 x 2 x 4
1 + 1 + 1 + 3 + 3= 1 x 1 x 1 x 2 x 4
1 + 1 +2 + 2 + 2= 1 x 1 x 2 x 2 x 2
Use the numbers 2, 3, 4 and 5 and the symbols + and = to make a true equation.
Conditions: Each must be used exactly once and no other numbers or symbols can be used.
There is a 5 gallon and a 3 gallon bottle. You also have a hose with unlimited water. How are you gonna make the 5 gallon have 4 gallons using your items?
(You don't know the exact dimensions of a gallon)
You fill the five gallon up and pour it into the 3 gallon. The dump the 3 gallon out and pour what was left in the 5 gallon into the 3 gallon so that you have 2 gallons in the 3 gallon. Then fill the 5 gallon up and pour it into the 3 gallon to fill it up. Now you have 4 gallons in the 5 gallons.
You're sitting in a car. The car has helium balloons tied to its floor. The windows in the car are closed and locked and the Air conditioner isn't working.
What will happen to the balloons when you press on the gas?
Will they move forward, stay in place, move backwards...?
The answer is they will move forwards.
Because helium is lighter than air, it will go where air isn't. When the car is pushed forward the air moves backwards, so the helium balloons will move to where the air is not - forward.
It comes only before,
It comes only after,
Rises only in darkness,
But rises only in light.
It is always the same,
But is yet always different.
What am I?
Four people need to cross a bridge in 17 minutes in the middle of the night. The bridge can only hold two or less people at any time and they only have one flashlight so they must travel together (or alone). The flashlight can only travel with a person so every time it crosses the bridge it must be carried back. Tom can cross in 1 minute, John can cross in 2 minutes, Sally can cross in 5 minutes, and Connor can cross in 10 minutes. If two people cross together they go as fast as the slower person.How can they cross the bridge in 17 minutes or less?
First Tom and John will cross (2 minutes). Then Tom will bring the flashlight back (1 minute). Next Sally and Connor will cross (10 minutes). Then John will bring the flashlight back (2 minutes). Finally John and Tom will cross (2 minutes). 2 + 1 + 10 + 2 + 2 = 17 minutes.
1 duck saw 4 elephants as it was going toward the river.
Every elephant noticed 2 monkeys going to the river.
Every monkey was carrying 1 dove in its paws.
How many animals are going to the river?
Five animals are moving toward the river.
Here's a detailed answer:
1 duck noticed 4 elephants as it was going toward the river. Hence, 1 animal (the duck) is moving to the river.
The 4 elephants saw 2 monkeys going walking toward the river. Now comes the tricky part. You may think that each elephant saw 2 different monkeys walking toward the river. So you would conclude that 4 x 2 = 8 monkeys were going to the river.
However, the task does not explicitly say that each elephant saw DIFFERENT monkeys. In fact, you can logically infer that the elephants saw the SAME 2 monkeys. Hence, we only have 2 additional animals (monkeys) moving toward the river.
Since every monkey was carrying 1 dove, the 2 monkeys were carrying 2 doves in total.
Summing up, we have 1 duck, 2 monkeys, and 2 doves moving to the river. 1 + 2 + 2 = 5 animals.
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