Category Archives: Arithmetic

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.

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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:
Toot 5x5 2015-04-24 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:
Toot 7x7 2015-04-24 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:
Toots 9x9 2015-05-15 nr 1

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**/*****

coupleAges**/*****
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.

1-8


The Dutch reformed-christian ‘Reformatorisch Dagblad’ twice a year publishes an extra puzzle issue for its subscribers. This weeks puzzle type is 1-8, invented by Marijke Balmaekers, and published in the childrens section of the ‘Vakantie Doe Boek’ of the reformatorisch Dagblad.

The numbers one to eight have been arranged in a 5×5 grid in such a way that:


  1. Each of the numbers one to eight is used exactly once

  2. There are always one or two numbers in every row, column or diagonal

  3. the sum of the numbers is listed as a clue at the end of the row/column/diagonal

Example:
1-8 example

number 1
1-8 2016-02-14 nr 1 exercise

number 2
1-8 2016-02-14 nr 2 exercise

number 3
1-8 2016-02-14 nr 3 exercise

You can check your solutions here, here and here

The online exam


certificate illustration
This week I’ve got a quickie for you.
Last week I took an online certification exam. It was an open book certifiction, and I was free to consult the website and course map as often and as long as I wanted. Some types of questions scored 3 points, others scored 5 points.

My result was:
You scored 201 points out of 223 total possible points.
You answered 45 out of 51 questions correctly.

How many 5-point questions and how many 3 point questions did I miss?

You can check your solutions here

A new puzzle is posted every friday. You are welcome to comment on the puzzles. Solutions are added at the bottom of a puzzle after one or more weeks.