DIALOGUE Issue #2 2017
84
THE GAMES ROOM Chess Problems with thanks to Alan Thorn These two positions are in games from our current top school players: Harry Grieve* (captain) (L6) and Alex Golding (Third Form). In the first diagram can you see how Alex (playing white) was able to force checkmate? In the second diagram can you see how Harry (playing black) was able to win material? Answers on p.89 * Harry Grieve was crowned 2017 UK Junior Chess Champion after seeing off the challenge of 45,000 participants in the Delancey UK Schools Chess Challenge.
Maths Conundrum: Pent Up by Mash Clues give the prime factorisation of answers to be entered. Each letter within a clue represents a distinct prime number, but not necessarily the same one throughout the puzzle. Factors are given in order of largest powers rather than size. Thus p alone means a prime number, p 3 would be the cube of a prime, and p 2q is a prime squared multiplied by another prime, such as 18 or 28.
No clued answers have leading zeros, all entries (clued and unclued) in the initial grid are distinct and all entries have at least two distinct digits.
The completed grid contains five distinct digits twelve times each. Further bars must then be inserted along gridlines to divide the grid into twelve distinct pentominos (see below) such that no digit is repeated within each. The bars already provided are the only ones from the final pattern that fall diametrically opposite each other.
F
I
Answers on p.89
L
N
P
Solvers may wish as a finale to highlight eight digits in two symmetrically placed sets of four (involving five pentominos). The difference between these two sets (an anagram of one unclued entry) can be entered in the central square to commemorate a recent event.
T
For anyone unfamiliar with pentominos, the full set is shown below, using their standard letter codes for reference. Rotations and reflections are allowed in this puzzle.
U
V
W
X
Y
Z
1
2
3
4
5
6
13
14
7
8 9
10
11
12 15 17
16 18
19
20
21 22
23
Across 1 pq 8 p5q2r 9 p3q3r 11 pqr 13 p2q 15 p 17 pqr 20 p2q2 21 p2q 23 pq
Down 1 pqrst 2 pqrs 3 p9 5 pqr 6 p 7 p4 10 p5q2r 14 p2qrs 18 p3 20 p3qr
