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?
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.
You have been given the task of transporting 3,000 apples 1,000 miles from Apple-York to Strawberry-Ville. Your truck can carry 1,000 apples at a time. Every time you travel a mile towards Strawberry-Ville you must pay a tax of 1 apple but you pay nothing when going in the other direction (towards Apple-York).
What is highest number of apples you can get to Strawberry-Ville?
833 apples.
How to solve:
You need to make 3 trips of 1,000 apples - 333 miles. You will be left with 2,001 apples and 667 miles to go.
Next you want to take 2 trips of 1,000 apples 500 miles. You will be left with 1,000 apples and 167 miles to go (you have to leave an apple behind).
Finally, you travel the last 167 miles with one load of 1,000 apples and are left with 833 apples in Strawberry-ville.
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
Janie's friends were chipping in to buy her a wedding shower present. At first, 10 friends chipped in, but 2 of them dropped out. Each of the 8 had to chip in another dollar to bring the amount back up. How much money did they plan to collect?
A businessman buys a horse for $10 and sells it for $20. He then buys the same horse for $30 and sells it for $40.
How much has the businessman earned in these 2 deals?
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?
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.
Start both hourglasses then when the 11 minute hourglass has finished immediately flip it again. When the 13 minute hourglass runs out the 11 minute hourglass will have 9 minutes left, so flip it and it will last another 2 minutes, 13 minutes + 2 minutes = 15 minutes.
7.5 degrees.
The minute hand is pointing directly at the '3'. The hour hand is 1/4 of the way between the '3' and '4'. Since there are 12 numbers the angle between each number is 30 degrees. So the angle between the hands are 30 degrees * 1/4 = 7.5 degrees.
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.
Walking home one day, you take a short cut along the train tracks. The tracks cross a narrow bridge over a deep gorge. At the point you are 3/8 of the way across the bridge, you hear the train whistle somewhere behind you. You charge across the bridge, and jump off the track as the train is about to run you down. As it happens, if you had gone the other way, you would have reached safety just before being run over as well. If you can run ten miles per hour, how fast is the train moving?
The train is moving at 40 miles per hour.
if there was a dog going towards the train while you go away from it as the whistle blows, he will reach his point when you are 3/4 (6/8) of the way on the bridge, the train will have just reached it. So for the train to cross the bridge at a rate four times yours it will have to be moving 4 times as fast.
You turn the 7 minute one and the 11 minutes one at the same time. When the 7 one finishes, turn it again. When the 11 one finishes, you know that 4 minutes have passed, with 4 minutes to get to the desired 15, all you need to do now is turn the 7 minute hourglass again since it counted 4 minutes, and when it runs out it'll be exactly 15 minutes.
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