square sums

1) 3×3
Every row and column adds up to 50
Complete the square with the indicated numbers – those who have been given are already crossed out for you.

2) 4×4
Every row and column adds up to 50

3) 5×5
Every row and column adds up to 100.

This type of puzzle was published in Cijfervaria, a publication of Sanders Puzzelboeken. As I write this, they just published issue 5. Though I missed issue 4, I see they regularly publish Soduko variants, Binairo, Triairo, hitori, and battle ship.

You can check your solution here, here and
here.

Did you know…
Learning new tasks saves brain cells – even if these tasks are more or less similar to already known tasks.

Four fours

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Using exactly four fours, create the numbers 0-30. You may use the usual mathematical operands, but not squaring, as this requires a number 2. You may use brackets.
Example: (4+4)-(4+4)=0

As always, please don’t publish your solutions. Solutions can be found after 1-2 weeks on the solution page for those who want to check their solutions, or for those who are really stuck.
But scrolling is much easier, and really spoils the fun for others.

I am very much interested in your solution times, and I welcome your remarks and criticisms. Pointing out alternative solutions is also welcome, as they point out possible problems in the brain teasers.

If you are puzzled, we have a solution for you.

This puzzle has a long history. When I still was a teenager, my father challenged me to make all numbers 0-20 using the digit 4 exactly 4 times. Recently I shared this puzzle with some fellow consultants. Kees Krol arrived at the office one morning and announced he had extended the range all the way to 30. 🙂

Strange calculation?

 

 
IF

8 x 2 = 46416
6 + 3 = 23618
15 : 3 = 513545
9 – 3 = 38127

Then what is :
12 x 4 =?

I am very much interested in your solution times, and you are welcome to make remarks, and discuss alternatives. Pointing out alternative solutions is also welcome, as they point out possible problems in the brain teasers, but please dont mention solutions and leave others the fun to solve them too.

If you are puzzled, we have a solution for you.

81

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Using four times the number four, create the number 81. You may use the usual mathematical operands.

If you are puzzled, we have a solution for you.

I would like to thank Kees Krol again for coming up with this one.

As always, please don’t publish your solutions. Solutions can be found after 1-2 weeks on the solution page for those who want to check their solutions, or for those who are really stuck.

But scrolling is much easier, and really spoils the fun for others.

Playing with numbers – quickies

The next two problems are variants of easy problems from the Dutch 2008 Mathematics Olympiad.
1) 2016^*
What is the smallest integer number that, when multiplying its digits, gives 2016?

2) Odd numbers ^*
Multiply all numbers between 1913 and 2012 (including 1913 and 2012). What is the last digit of the product?

You can check your solutions at 16 and 26 respectively.