Puzzle of the Week #261 - Su-Dot-U

Your task is to solve this irregular sudoku (the digits 1 to 5 appearing once each in every row, column and 'shape').
Except that I haven't told you where the boundaries between the shapes are; instead I've placed dots in any square where the number to be placed in the square denotes how many squares (including the one with the dot in) until you get to the next boundary line in the direction of the dot.
Clear as mud? Hopefully the attached example 3x3 will help. For instance, the 2 in the middle of the top row, combined with the left and right dots, says that in each direction left and right from that square there are two squares (including the one with the 2 and the dots in) before you get to a boundary line (which happens to be the outer boundary of the entire grid).
In both the example and the puzzle, I have placed dots in every position that I could, according to the rules.

A hint to get you started: if a dot appears next to the outside boundary of the grid, then that square must contain a 1.

sudotu3.JPG

Puzzle of the Week #260 - Semi-grams

Rearrange the letters in each of these ten five-letter words and then pair them up to form five ten-letter words. I’ve completed one of the ten letter words to start you off:

First halves:

(ALERT)    METRO    NOTED TIMES    UPSET

Second halves:

GIANT    (RATIO)    ROAST SENSE    SOUND

Example solution:

ALERT + RATIO = RETAL + IATOR = RETALIATOR

Puzzle of the Week #258 - Su-Dot-U

Back by popular demand!

Your task is to solve this irregular sudoku (the digits 1 to 6 appearing once each in every row, column and 'shape').

Except that I haven't told you where the boundaries between the shapes are; instead I've placed dots in any square where the number to be placed in the square denotes how many squares (including the one with the dot in) until you get to the next boundary line in the direction of the dot.

Clear as mud? Hopefully the attached example 3x3 will help. For instance, the 2 in the middle of the top row, combined with the left and right dots, says that in each direction left and right from that square there are two squares (including the one with the 2 and the dots in) before you get to a boundary line (which happens to be the outer boundary of the entire grid).

In both the example and the puzzle, I have placed dots in every position that I could, according to the rules.

A hint to get you started: if a dot appears next to the outside boundary of the grid, then that square must contain a 1.

sudotu 2.JPG

Puzzle of the Week #256 - Su-Dot-U

Your task is to solve this irregular sudoku (the digits 1 to 5 appearing once each in every row, column and 'shape').
Except that I haven't told you where the boundaries between the shapes are; instead I've placed dots in any square where the number to be placed in the square denotes how many squares (including the one with the dot in) until you get to the next boundary line in the direction of the dot.
Clear as mud? Hopefully the attached example 3x3 will help. For instance, the 2 in the middle of the top row, combined with the left and right dots, says that in each direction left and right from that square there are two squares (including the one with the 2 and the dots in) before you get to a boundary line (which happens to be the outer boundary of the entire grid).
In both the example and the puzzle, I have placed dots in every position that I could, according to the rules.

A hint to get you started: if a dot appears next to the outside boundary of the grid, then that square must contain a 1.

su-dot-u.JPG

Puzzle of the Week #253 - Build-a-Crossword

I have taken a completed crossword grid, removed all the consonants to the end of the row and/or column that they belong in, and then changed all the black squares into random vowels.

Your task is to reconstruct the crossword by figuring out which of the vowels are genuine and which need to become black squares, and by putting the consonants all back into place. Good luck!

BUILDACROSSWORD PUZ.JPG


Puzzle of the Week #251 - Trispace

I have an equilateral triangle, dissected into three trapezoids and a smaller equilateral triangle. The PERIMETERS of the three trapezoids are 52, 66 and 80 respectively. The side length of the overall equilateral triangle (a) is precisely 13 times the side length of the smaller equilateral triangle (b).

What is the value of a?

trispace.JPG

Puzzle of the Week #248 - Quartet

The four numbers 2,3,4 and 8 can be combined in pairs in six different ways, and the product of those six pairs will be

2 x 3 = 6

2 x 4 = 8

3 x 4 = 12

2 x 8 = 16

3 x 8 = 24

4 x 8 = 32

The sum of the original four numbers (2, 3, 4 and 8) is 17.

Can you find a different quartet of POSITIVE numbers whose products of pairs are also 6, 8, 12, 16, 24 and 32, but whose sum is less than 17?

Puzzle of the Week #246 - Ghost Crossword

Use logic to fill in the crossword grid given only the clue numbers and the following rules:

1) The crossword is numbered in the usual way.

2) The grid is fully symmetrical.

3) The white area must all be connected together.

4) ‘Words’ are at least three letters long.

5) No 2x2 black squares are allowed.

6) No row or column is entirely white or entirely black.

ghost puz with numbers.JPG


Puzzle of the Week #245 - Three Digits

I have three digits A B C, such that A is less than B, which is less than C. I can arrange these to form six different 3-digit numbers.

When A is at the start, both possible numbers (ABC and ACB) are prime.

When A is in the middle, both numbers are semi-prime (the product of two prime numbers).

When A is at the end, the number is either abundant by 71 (the sum of its proper divisors is 71 more than the number itself), or deficient by 226 (the sum of its proper divisors is 226 less than the number itself).

What are the three digits?

Puzzle of the Week #244 - Three Way Split

Given a unit square it is possible to split it into three equal areas in a number of different ways. For instance cutting off the top third and then the bottom third. Or cutting off the top third then making a vertical cut to divide the remaining part in two. The total cut length of that first option is 2, whereas the total cut length of the second option is only 1+2/3.

Can you find a way of dividing the square into three equal areas, which requires even less total cut length?

cut sq 3.JPG

Puzzle of the Week #243 - Shaded Circles

A circle of radius 2 has a circular hole of radius 1.

This is done is two alternative ways: in one the hole is tangent to the larger circle forming a crescent shape; in the other the hole is in the exact centre of the larger hole.

In the ‘crescent’ option a shaded circle of radius 1 is drawn, and then infinitely many smaller and smaller shaded circles are added heading off towards the two tips of the crescent.

In the ‘ring’ option just nine circles, each of radius ½ are drawn and shaded.

Which version has the largest combined shaded area?

shaded circles.JPG