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.
1. Each letter represents a different digit from 1 to 9 2. The total of each row is 17. 3. (B × B) + B + F = A 4. C × F = EF (a 2-digit number, not their product)
A + B + C = 17 D + E + F = 17 B2 + B + F = A C × F = EF
To begin with, B has to be a 1 or 2 or else A wouldn’t be a single digit. Plug in B = 2, gives you 6 + F = A, meaning F and A can only be (1,7) or (3,9). To get 17, C would have to be 8 or 6, but those values don’t work for C × F = EF. So B must be 1.
2 + F = A means F and A can be (2,4), (3,5), (4,6), (5,7), (6,8) or (7,9). To get 17 on the top row, the only option that leaves C as a single digit is F = 5 and A = 7.
C × F = EF 9 × 5 = 45, so E = 4 and D = 8 to make the second row equal to 17.
I’m a six-letter word. If I did not exist, you wouldn’t either. With my first letter omitted I’m an alternative. The last three letters are feminine. The first four letters make an insect.
Most of you have two eyes. I only have one. Most of you have eyeballs. I do not. Your eyes aren’t dangerous, neither are mine. But all together, I am extremely dangerous. You can see things with your eyes. I can’t see anything, even though the air is clear where my eye is.
At the market you can buy a cow for $10, a pig for $1 and 8 hens for $1. How many animals would you need to buy to get 100 mixed animals for exactly $100?
7 cows, 21 pigs and 72 hens. The trick to this is finding the combination of cows and hens with the same cost and quantity since pigs are already equal. The magic combination is 7 cows and 72 hens, giving you 79 animals that cost $79 ($70 + $9). Then you just add 21 pigs to get to 100 animals.