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
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.
We have two soap of equal weights and a 3/4 pound weight.
However, after using 1/4 of soap we place all three objects on balance as On one side of balance we place one soap (unused) and on another side, we placed used soap (i.e 3/4th of soap) and 3/4 pound weight.
What is the soap weight?
Placed above it makes greater things small.
Placed beside it makes small things greater.
In matters that counts it always comes first.
Where others increase it keeps all things the same.
What is it?
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...
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.
An ant gets onto one end of a tight rope that is 1 meter long. The ant is traveling at 1 centimeter per second, but the entire rope is being stretched an extra 1 meter (1,000 centimeters) a second (it can be stretched forever).
Will the ant ever reach the other end of the rope?
The rungs of a 10 foot ladder attached to a ship are 1 foot apart. If the water is rising at the rate of one foot an hour, how long will it take until the water covers over the ladder?
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.
You are distributing vegetable oil. There are 21 bottles in total out of which 7 are full, 7 half empty and 7 empty. The oils has to be distributed among three people.
How will you distribute so that each person gets equal number of bottles and the same quantity of oil?
First Person: 3 full bottles, 1 half empty bottle and 3 empty bottles.
Second Person: 3 full bottles, 1 half empty bottle and 3 empty bottles.
Third Person: 1 full bottle, 5 half empty bottles and 1 empty bottle.
Ben has math lessons 4 times a week. If he has math 8:00 Monday, 9:20 on Tuesday, 10:40 on Wednesday, and 1:20 on Friday, when does Ben have math on Thursday?
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.
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