Resolf

Resolf puzzles consist of four triangles, with three numbers at the corners of each triangle and the sum of the three numbers in the center.

I first encountered them in a publication by Sanders Puzzles.

An example of a solved resolf looks like this:

Nr 1^*/*****
Use the numbers listed below the triangle to make the sums

Sanders puzzles regularly also uses multiplcation:
Nr 2^**/*****

And one can extend this machanism to all 40 basic arithmetic operations:
Nr 3^***/*****

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Clocks and time

There are many, many puzzles about clocks and time. In the nineteenth century, both Henry Dudeney and Sam Loydd designed a number of them, and in a future post I may collect them.

1) Basics^*/*****
Today I encountered this problem on twitter, posed by a teacher for his students in primary school. Whisper your solution in the ear of the teacher to enter the classroom.

2) Advanced^***/*****

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Pluszle

Pluszle® is the trademarked name of a new type of number puzzle I encountered in the book/magazine shop at The Hague CS. I didnt want to buy it, but today my wife bought me a copy. The rules for the puzzle are elegantly simple. The grid is filled with numbers, and you have to cross out numbers till the sum of the remaining numbers equals the numbers in the right and bottom margins.

1) 5×5 nr 1^*/*****

2) 5×5 nr 2^**/*****

3) 6×6 nr 2^**/*****

Priced at 4,95 euro and containing 375 puzzles it doesn’t sound like a bad deal. The main problem seems to me that the first part of the booklet contains 3×3 and 4×4 puzzles. In my humble opinion, these could have been omitted. Just this morning I was tweeting about education, automation of arithmetic, and differentiation in exercises for different students. Maybe I would have loved it to get puzzles like these at primary school as extra exercises.
The booklet is produced by Pluszle BV in Leusden, and outsider in the Dutch puzzle magazine world, which is dominated by Denksport and Sanders puzzels. Their website at http://www.pluszle.com mentions apps for the I-store and the android store, but I must admit I didn’t try the app.

Another, albeit smaller problem, is that the main variation is the size of the grids: the larger the more complex. It isn’t too difficult to create similar problems with multiplication:
4) 5×5 nr3^*/*****

Another variation I can think of is a 4×4 grid with subtraction: cross out two numbers in every row and column so that the difference is the number in the right or bottom margin.

There is an even more puzzling form, but I think I reserve that for a subsequent post.

Now my words above may sound like a negative judgment, but I do not intend them to be that way. The larger sizes 6×6 and above, do offer a fair agree of difficulty.

Solution strategies
There are several solution strategies, here are the main ones:



(a) 8 can not be there, >5
(b) 3 can not be there, not in any combi
(c) 6 must be there, else you can not add up to 15
(d) all numbers must be there

Alice and the sweets

This week we have an honoured guest – Alice. Yes, Alice from Alice in Wonderland!
Alice heard Tweedledum say: Yesterday we got a number of wine gums. We both got the same number, but we played a game which I won and then I had 5 times as many wine gums as Tweedledee. But when I gave him one of my wine gums, I had only 4 times as many wine gums as he had.

This week we have an honoured guest – Alice. Yes, Alice from Alice in Wonderland!
Alice heard Tweedledum say: Yesterday we got a number of wine gums. We both got the same number, but we played a game which I won and then I had 5 times as many wine gums as Tweedledee. But when I gave him one of my wine gums, I had only 4 times as many wine gums as he had.

1) How many wine gums did Tweedledee and Tweedledum have?

That’s strange, Alice said. Yesterday, I mean the day before I fell into this rabbit hole, I had been playing a game with my sister. We were playing for matches, and after the game I had 7 times as many matches as my sister. But when I gave her one of my matchsticks, I had only 6 times as many matches.

2) How many matches did Alice and her sister have?

I was telling the story above to a little girl called Alais. Alais thought for a moment, then told me: That is strange. Yesterday, the day before you told me this puzzle, I was playing a game with my little sister. After the game, I had 10 times as many gumdrops as she had. Of course I gave her one, and then I had exactly 9 times as many as she had.

3) Alais is obviously a very smart girl. I knew she had had some elementary algebra at school. She had obviously figured out that there are an infinite number of numbers with which this puzzle can be told. Can you explain why?

You can check your solution here

New puzzles are published at least twice a month on Fridays. Solutions are usually published after one or more weeks.

Which number

What is the smallest number that has a remainder of 2 when divided by 14, 18 and 32?

You can check your solution here

New puzzles are published at least twice a month on Fridays.

Hidden numbers

In issue @@@ of @@@, Sanders published a new type of puzzle, called ‘hidden numbers’.

I must confess that the puzzle was too hard for me, though in the future I may give it a try again.

In this post I present a simplified version.
1. The numbers 1 to n have been hidden in a square grid.
2. Yellow areas give the sum of the hidden numbers in row and column of the yellow square.

Example:

1) 4×4^*/*****

2) 5×5^*/*****

3) 6×6^**/*****

From here there are two ways to increase the difficulty of the puzzle (aside from increasing the size):
a) Put more than one hidden number in a row and / or column. This is what Sanders did.
b) Sum only the first number visible in any row or column. Any number, including the numbers in yellow squares, block the line of sight for any numbers behind them.

New puzzles are published twice a month on Fridays. Solutions are published after one or more weeks. You are welcome to discuss difficulty levels, variations and alternate solutions, but plz. don’t publish the solutions.

TooT

In this post I’d like to introduce TooTs, a mix between crossword puzzles and numbers. The grid looks just like a crossword puzzle, but instead of words the grid has to be filled with numbers. Vertical numbers must be read top-down. Thus if the digits 3, 9 and 5 are listed from the top down, the number would be 395.

Every clue consists of three numbers. Two of them have to be added together to get the number to be filled into the grid.
Example: the clue is 7, 8 and 13. Then the solution is either 7+8=15, 7+13=20 or 8+13=21. The name TooT is shorthand for Two out of Three.

Here is a 5×5 exercise:

Horizontal 1) 16, 17, 18 3) 20, 26, 36 4) 142, 139, 145 8) 6819, 20002, 30134 11) 18, 20, 22 12) 11, 24, 36

Vertical 2) 17, 19, 23 3) 18, 36, 47 5) 400, 406, 418 6) 18, 106, 256 7) 15, 25, 190 9) 1, 51, 61 10) 11, 12, 13

A 7×7 exercise:

Horizontal 1) 16891 18930 6) 382, 23, 67 8) 25, 8, 17 10) 32, 14, 17 11) 2913476, 173823, 1876543 12) 61, 23, 38 13) 45, 11, 34 14) 865, 249, 444 16) 13947, 1171, 5419

Vertical 2) 53, 26, 27 3) 8843269, 332160, 345612 4) 22, 3, 5 5) 12263, 5321, 6942 7) 62652, 23487, 39165 9) 591, 109, 482 10) 374, 25, 98 14) 83, 16, 26 15) 54, 17, 27

You can check your solution here and here

A 9×9 puzzle:

Horizontal 1. 108, 132, 146 4. 2, 166, 660 6. 2497, 9892, 12837 9. 0, 7, 24 11. 212, 669, 774 12. 4, 19, 30 13. 18, 27, 27 15. 14, 33, 40 16. 242, 977, 2236 17. 596, 903, 2770 18. 25, 31, 52 20. 4, 11, 22 21. 7, 9, 35 22. 126, 343, 422 24. 3, 10, 13 26. 2918, 74181, 82214 28. 292, 320, 398 29. 66, 191, 228

Vertical 1. 38, 96, 224 2. 4, 41, 77 3. 239, 1644, 4146 4. 19, 29, 35 5. 3, 7, 227 7. 20, 36, 38 8. 1, 14, 17 10. 12591, 13966, 31881 12. 706, 10961, 36955 14. 186, 210, 367 15. 102, 153, 279 19. 2287, 3330, 3945 21. 112, 239, 304 22. 19, 26, 45 23. 6, 23, 87 25. 74, 299, 315 26. 33, 49, 52 27. 12, 12, 12

You can check your solution here and here

In a subsequent post, probably next month, I hope to publish some variations.

Ages

Ages^**/*****

Ages^**/*****
A man is 25 years old and his wife 23. He noticed that the sum of their ages (25+23=48) is exactly 4 times the sum of the digits of their ages. (2+5+2+3=12).

When will the sum of their ages be exactly 8 times the sum of the digits of their ages? And when will it be 9 times the sum of the digits?

You can check your solutions here

New puzzles are published at least twice a month on Friday. 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.

3 3’s

Use 3 3’s to make exactly 20.
Hint: USA inhabitants have it easier.

You can check your solutions here

A new puzzle is published every Friday.

My colleague and his daughter

This week a colleague brought some cake for his birthday. He didnt want to tell his age, but he did reveal that he and his daughter together were 46 years old, and that in eleven years he would be thrice as old as his daughter.
What are their ages?

You can check your solutions here