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.
The word One has 3 letters, in the word three there are 5 letters, in the word five there are four letters and four has four letters in it as well. Whatever number you'll go back to four, and that's why it's the magic number.
You want Bob to have your phone number, but for some reason you can't ask him directly. You have to write Bob a note, and pass it to him through Lucy. Lucy can give you a note back with Bob's reply, but you don't want Lucy to know your phone number herself.
What will you write on the note to Bob?
This has several options for a creative mind. Our solution? Ask Bob to call you at a certain time, that way you'll know it's him and you can save the phone number.
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.
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.
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?
The next number should be 13112221. Why?
Because each of these numbers describes the previous number. Starting with 1, the 2nd line is 11 (one one), then the 3rd line describes 11 as 21(two ones). Then the 4th line is 1211 which describes (one 2, one 1). And so forth...
A new medical building containing 100 offices had just been completed. Mark was hired to paint the numbers 1 to 100 on the doors. How many times will Mark have to paint the number nine?
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
A man was found dead while on his work trip abroad. The suspects were his colleagues Mason, Bob, Lisa, and Alex. On the calendar, 3, 4, 9, 10, 11 were written in blood. How should the detectives decode the numbers to find the killer?
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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