Maths crossword puzzle

RoundTower

I was going through some of my old stuff and found this puzzle, I think it's amazingly well done. It was originally published as a "Listener" crossword in the Times of London in 1994.

Not sure if this is the best place to post this puzzle, or if it's been posted before, but it might be too difficult for the puzzles/quizzes forum. No advanced mathematics or crossword experience is necessary, just a lot of deductive reasoning.



The following statements about the numbers 1 to 50 are also true about their associated lights.
No number begins with zero.
All the numbers are different.

Only 1, 4, 9, 16, 25, 36 and 49 are perfect squares.
Only 1, 8 and 27 are perfect cubes.
Only 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47 are prime numbers.
Only 11, 22, 33 and 44 are palindromes.
7 < 20 < 24
7 is a factor of 14, 21 and 35
8 is a factor of 48
9 is a factor of 45
11 is a factor of 44
12 = 9 + 3
15 = 10 + 5
16 < 25 < 36
22 = 11 + 11
23 is a factor of 46
27 = 18 + 9
Digit sum of 28 = digit sum of 19
28 = 7 + 7 + 7 + 7
Digit sum of 30 = digit sum of 12
Digit sum of 31 = digit sum of 13
32 = 26 + 6
Digit sum of 32 = digit sum of 23
33 = 31 + 2
Digit sum of 33 < digit sum of 16
Digit sum of 34 = digit sum of 25
Digit sum of 35 = digit sum of 17
36 = 9 + 9 + 9 + 9
Digit sum of 38 = digit sum of 29
38 < 39 < 40
41 = 23 + 18
41 < 42
Digit sum of 42 < digit sum of 36
Digit sum of 46 = digit sum of 37 = twice digit sum of 23
49 = 25 + 24
Digit sum of 50 < digit sum of 24.

LeixlipRed

That looks cool alright. Must print it off and give it a shot later.

hivizman

The "Listener" Crossword in The Times has a mathematical theme four times a year (the fourth weeks of February, May, August and November). The last mathematical puzzle (28 February 2009) involved trying to fit the 12 pentominoes (all possible shapes of five contiguous squares) into a 5 x 12 rectangle, with each pentomino being numbered from 0 to 11. Each square on a particular pentomino was given the number of the pentomino, and the clues were the products of the numbers in each row and in each column.

RoundTower

hivizman wrote: »

The "Listener" Crossword in The Times has a mathematical theme four times a year (the fourth weeks of February, May, August and November). The last mathematical puzzle (28 February 2009) involved trying to fit the 12 pentominoes (all possible shapes of five contiguous squares) into a 5 x 12 rectangle, with each pentomino being numbered from 0 to 11. Each square on a particular pentomino was given the number of the pentomino, and the clues were the products of the numbers in each row and in each column.

I didn't know this, assumed the one I had was a once off because the word-based ones are utterly impossible. I'll keep an eye out for the future maths ones