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.

Fibonacci series

Today’s puzzles were inspired by Michael Jacobs “Introductory Thinking Tasks”.

You all know the Fibonacci series: a term is the sum of the two previous terms, with the first two given. The top row shows a classic sequence:

Your task is of course to fill in the empty spaces of the other two rows.

New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solution here.

The sum of the digits

If you think that mathematics and arithmetic is something for boys, you probably never read about Shakuntala Devi. Born in 1929, as a young child she was taken by her father on road shows to display her abilities for mental calculation. At the age of six she demonstrated her abilities at the University of Mysore.

In 1977, when she must have been 48, at Southern Methodist University, she gave the 23rd root of a 201-digit number in 50 seconds.[6][4] Her answer, which was 546,372,891, was confirmed by calculations done at the US Bureau of Standards by the UNIVAC 1101 computer, for which a special program had to be written to perform such a large calculation, which took a longer time than for her to do the same.

She wrote several books, on puzzles, astrology, memory and homosexuality. What interests us here is the book “Puzzles to puzzle you”.
Here is one of them:
Which number is exactly 3 times the sum of its digits?

In her honor :
Which number is exactly 11 times the sum of its digits?

You can check your solution here

Four equal sized areas

This week we have some calculation problems for you.

1) four areas 4×6^**/*****
Divide this grid into four equal sized areas, each with the same sum.

2) four areas 4×7^**/*****
Divide this grid into four equal sized areas, each with the same sum.

You can check your solutions here.

New puzzles are posted twice a month on Friday. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solutions here.

What’s next?

1) Next^*/*****
What is the next number in the series 17, 72, 28, 83, 39, 94, 50, 05, 61, …

New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solutions here.

2021

Happy 2021!
May G’d bless you.

I sincerely hope that 2021 will bring an end to the Covid-19 crisis which plagued us in 2020.

For the past couple of year I present you some puzzles which have to do with the number of the new year, in this case 2021.

1) Sum 5^*/*****
how many 4-digit year numbers are there with the sum of the digits is 5? (No leading zero’s allowed)

2) two consecutive primes (i)^**/*****
2021=43*47, two consecutive prime numbers.
There are just two 4-digit numbers which are the two products of 2 consecutive primes and have a 0 in them. 2021 is one of them. What is the other one?

3) sum of factors (ii)^**/*****
2021=43×47, two primes.
The sum of the prime factors of 2021 is 1 + 43 + 47 + 2021 = 2112.
That gives a sum consisting of just 2 different digits. What is the next year that has a sum of its factors that is made up of just 2 different digits?

3) sum of prime factors (iii)^***/*****
The sum of the prime factors of 2021 is 1 + 43 + 47 + 2021 = 2112. 2112 is a palindrome.
What is the next year (product of two primes) in which the sum of its 4 factors is a palindrome?

4) The square of 2012 is 4084441^*****/*****
4084441 consists of 4 different digits. What is the first year in which the square consists of 3 different digits?

5) Bongard problem 2021-1^****/*****

In a Bongard problem, all the pictures on the left share a common property. None of the numbers on the right has this property. What is this property?

6) Bongard problem 2021-2^***/*****

New puzzles are published at least once a month on Fridays. Solutions are published after one or more weeks. You are welcome to remark on the difficulty level of the puzzles, discuss alternate solutions, and so on. Puzzles are rated on a scale of 1 to 5 stars. You can check your solutions here.

What’s next

This weeks quickie is inspired by a tweet by Laurie Rubel.
What’s next^**/*****
14, 17, 23, 24, 26, 30, 33, …

A new puzzle is published at least twice a month on Friday. You can check your solution here.

Quento

While cleaning up old newspapers in someone’s house I came across a puzzle called “Quento” in the Dutch newspaper “Algemeen dagblad”.

The basics of this puzzle are simple calculations. What sets it a bit apart from other puzzles is that the answers are given, and that you have to find the exercise.

Example:

You have to find a calculation for each of the numbers on the right by going from a number to a + or – sign and on to another number. If necessary, you may add additional +/- signs and numbers, as long as you don’t use the same number or sign twice.

What you may do:

Not allowed is:

Of course there is a website, and an app for both Android and Ipad. Personally I think the exercises are too easy, though no doubt they can be increased by adding size and moving to higher numbers, as shown in our 4th problem. In the app I did see higher numbers, in the sense of multiples of 3, 4, 5 , and so on, but I didn’t see larger sizes, as in our fourth problem. That may be because I didn’t purchase the app and just used the free version.

Quento 2^*/*****

Quento 3*/*****

Quento 4**/*****

You can check your solutions at href=”https://justpuzzles.wordpress.com/Solutions to puzzles 501-750/#516″>here.