You want to go on an adventure to the remote city of Chenarz, but it’s 120 miles off the Pacific coast. To conserve money, take the smallest number of people as possible. Each person can carry enough food for five days but you can only travel 30 miles a day. You want to reach Chenarz, stay overnight, and return the next day. How many people, including yourself, must you take to reach the city?
You will need three other members in your party to accomplish your mission for a total of four people.
Four people × 5 day’s rations = 20 day’s rations.
Day 1: 5 rations – Four day’s rations are used. One person goes back using one day’s ration for the return trip.
Day 2: 5 rations – Remaining three members use three day’s rations. One goes back using two day’s rations for the return trip.
Day 3: 5 rations – Remaining two use two day’s rations. One goes back using three day’s rations for the return trip.
Day 4: 1 ration – You use one day’s rations. You reach the city and stay the night.
Day 5: 4 rations – You return to the coast using up four day’s rations.
I go up, but at the same time go down,
Up toward the sky and down toward the ground,
I’m present tense and past tense too,
Come for a ride, just me and you.
You are decorating for spring and you’ve found a bargain. A huge box of beautifully decorated tiles, enough to provide a border in two rooms. You really can’t figure out how to arrange them. If you set a border of two tiles all around, there’s one left over. If you set three tiles all around or four or five or six there’s still one tile left over. Finally you try a block of seven tiles for each corner and you come out even. What is the smallest number of tiles you could have to get this result?
A dad offered to pay his son $5 for every correct answer on his math test. His son said he would pay his Dad $8 for every incorrect answer. There were 26 questions on the test and no money was exchanged.
The son got 16 questions correct and missed 10. This means he owed his Dad 10 * $8 = $80, but his Dad owed him 16 * $5 = $80, so it was a wash.
Two math equations to solve it are x + y = 26 and 5x = 8y.
A father gathered his three sons and told them he would die soon and needed to decide which son would inherit his land. He gave them the following test.
“Go to the market and purchase something that is large enough to fill my bedroom, but small enough to fit in your pocket. Based on what you bring I will decide which of you is wisest.”
All three sons went to the market in search of something to satisfy their father’s demands. When they returned the father gathered them in his bedroom.
The first son put down pieces of cloth that he had bought and laid them end to end across the room, but it barely covered any of the floor.
The second son laid down hay but there was only enough to cover part of the floor.
The third son showed his father what he had purchased and the father announced, “You are truly the wisest and will inherit my land.”