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.
When Julian and Penelope met, one was half the others age plus seven years. Ten years later when they married, Penelope was thirty, but this time one was nine tenths the age of the other. How old was Julian? (No fractions or partial years, whole numbers only).
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?