Category Archives: Numbers

Three cubes


In the picture above, when we calculate the sum of the three cubes on the left side, we see that two of the digits are present in the sum.

There are no 2-digit numbers which are equal to the sum of the squares of their digits.
There are 3-digit numbers which are equal to the sum of their third powers. Which are they?

(My sincerest apologies for not providing a link to a solution. WordPress has changed the interface and I have been unable to master it. I’m still looking for the right way to switch to html editing and add images and links)

Three squares


What number goes to the question mark?

1) Nr 1**/*****

You can check your solution here

2) Nr 2**/*****

You can check your solution here

3) Nr 3**/*****

You can check your solution here

New puzzles are published at least twice 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.

The animals in my house


Animals*/*****



In our house, we have more than two animals. All the animals in our house are dogs, except for two. All the animals in our house are cats, except for two. All the animals in our house are mice, except for two.

The puzzle comes from Grace Church school math problems.

New puzzles are published at least twice 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

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.

Find a 4 digit number


Number**/*****
Find a four digit number abcd such that
– abcd is a prime number,
– a+b+c+d = 10,
– the sum of the digits of ab*cd equals 7.

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.

On the first day of Christmas…


1) On the first day of Christmas**/*****
On the first day of Christmas, my true love brought to me:
On the first day of Christmas
My true love gave to me
A partridge in a pear tree

On the second day of Christmas
My true love gave to me
Two turtle doves
And a partridge in a pear tree

Thus go the first two couplets of a traditional Christmas song. Question is:
Haw many things did my true love give me over these 12 days? (counting the partridge in the pear tree as one item)

You can check your solutions here

2) On the second day of Christmas**/*****
Yeah, in puzzle 1 above you had the classical song. But in puzzle land, everything is different.
In puzzle land, on the second day of Christmas my true love brought me this puzzle:

“This puzzle consists of @ letters”

With what number (spelled out, of course) should @ be replaced to be true?

You can check your solutions here

3) On the third day of Christmas**/*****
On the third day of Christmas, my true love brought to me this puzzle:

“This puzzle consists of @ vowels and # consonants”

Again, by which numbers, spelled out, should @ and # be replaced to yield a true sentence? Please note that “y” is counted as a vowel.

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 three stars.

1000


A prime number is a number that can only be divided by 1 and by itzelf. Examples are 2, 3, 5, 7, 11, 13 and so on. You can find the first 1000 prime numbers here.

Now here is a quicky: write 1000 as the sum of as many different primes as possible.

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.

Odometer


Odometer problemThe display of the odometer in my car showed a number of five consecutive, decreasing digits. My mind wandered off. It was a nice number, of course. It was also clear what the next number with decreasing consecutive numbers would be, and how many kilometers I would have to drive. But what would be the next number that consisted of consecutive digits, and which also would be a prime number?

You can check your solutions here