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?
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.
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.
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?
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.
A magician is standing on a concrete floor holding a raw egg with his hand outstretched.
Without the aid of any other objects, he is able to drop the egg 2 feet without breaking its shell.
How did he do it?
You are on your way to visit your Grandma, who lives at the end of the valley. It's her anniversary, and you want to give her the cakes you've made. Between your house and her house, you have to cross 5 bridges, and as it goes in the land of make-believe, there is a troll under every bridge! Each troll, quite rightly, insists that you pay a troll toll. Before you can cross their bridge, you have to give them half of the cakes you are carrying, but as they are kind trolls, they each give you back a single cake.
How many cakes do you have to leave home with to make sure that you arrive at Grandma's with exactly 2 cakes?
The dog was wearing a 2-foot leash. When he saw a squirrel, he immediately started chasing it, and he was really able to catch the squirrel.
How did the dog succeed?
Mike has some chickens that have been laying him plenty of eggs. He wants to give away his eggs to several of his friends, but he wants to give them all the same number of eggs. He figures out that he needs to give 7 of his friends eggs for them to get the same amount, otherwise there is 1 extra egg left.
What is the least number of eggs he needs for this to be true?
301 eggs.
The number of eggs must be one more than a number that is divisible by 2, 3, 4, 5, and 6 since each of these numbers leave a remainder of 1.
For this to be true one less than the number must be divisible by 5, 4, and 3 (6 is 2*3 and 2 is a factor of 4 so they will automatically be a factor). 5 * 4 * 3 = 60. Then you just must find a multiple of 60 such that 60 * n + 1 is divisible by 7. 61 / 7, 121 / 7, 181 / 7, 241 / 7 all leave remainders but 301 / 7 doesn't.
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