2, 3, 4, 5

Two weeks ago we made a list of all the numbers we could make by combining the integers 1, 2, 3, and 4 with the common arithmetic operations +, -, * and /.

2, 3, 4, 5^***/*****
This week I challenge you to make the numbers 0 – 20 by using the digits 2, 3, 4, and 5 with the common arithmetic operators mentioned above.
If you are really stuck, you may use the “!” operator, but don’t use it if you can do without it.
In case you are not familiar with the !-operator:
2! = 2*1 = 2
3! = 3*2! = 3*2 = 6
4! = 4*3! = 4*6 = 24
5! =5*4! = 5*24 = 120.

New puzzles are published at least twice a month on Fridays. You can check your solution here.

1, 2, 3, 4

1) Use the digits 1,2, 3 and 4 each once to make all numbers 0 to 33. You may combine them in any way you want with +, -, * and /.
2) Proceed to 42 by also using exponents.

New puzzles are published at least twice a month on Fridays. You can check your solution here.

Alice and the pies

Alice and the March Hare had a Christmas lunch. Alice had baked 5 pies, the March Hare 3.
“It’s tea time,” the March Hare said. “So let’s eat the pies.”. The Mad Hatter popped in.
“It’s lunch time, not tea time,” Alice said. “But we can eat the pies.”
Each pie was cut into 3 parts, with one part eaten by each of the three.
“It was the best butter, you know” the March Hare said. “And there’s nothing better than the best butter, you can’t deny that.”
Alice looked surprised at him, as she didn’t understand why he made that remark.
“Well, I think they all are delicious”

At the end, the Mad Hatter thanked them, paid 8 pounds and left.

“Now that’s 5 pound for you and 3 for me,” the March Hare said.
But Alice doubted this was fair. Was Alice right?

I found this problem at https://plus.maths.org/content/sharing-cakes. Reportedly, a version of it was written by Ali ibn Abi Talib in the seventh century AD. Another version appears in Fibonacci’s famous Liber Abaci.

New puzzles are published at least twice a month on Fridays. You can check your solution here.