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In Chess, the Knight moves in an "L" shape. If the Knight was placed on square P in the diagram, it could move to any one of squares 1 to 8.
This week's puzzle is to find the SMALLEST number of knight moves needed to walk the knight from Square A to Square B, without going over the edge!
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Back to the chess board again this week, and time now to bring out
the dominoes. Each domino, by the way, covers two squares on the
board. It is easy to cover a normal chess board with 32 dominoes just
by making 8 rows of four dominoes. For this puzzle though, I have
removed two of the corners to leave 62 squares.
Can you find a way of covering the remaining squares on the board with just 31 dominoes?
Some people say it can't be done. Perhaps they haven't tried very hard!
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The game of "NIM" involves rows of matches laid out to make a triangle. When it is your go, you can take away as many matches as you like PROVIDED THEY ALL COME FROM THE SAME ROW.
You win if you force the other person to take the last match. The diagram above shows the game in mid-play. It is your go. Which match(es) should you take to win the game?
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Hungry Horace (yes, he's back!) went into the Music Shop to buy some musical sweets which they were selling.
There were three special packs on offer:
1) Ten minims and five crotchets: 35p (save 5p)
2) Ten crotchets and ten quavers: £1 (save 20p)
3) Thirty minims: 50p (save 10p)
What would be the full price of one minim, one crotchet and one quaver?
(Clue: Ask your music teacher about the number of notes in a 4/4 bar!)
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How can I cut the board into only two pieces so that they will cover the hole exactly?
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The diagram shows 3 squares and 2 triangles.
Rearrange the matches to make 5 squares and 6 triangles.
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Hungry Horace was looking through the family photograph album, which has one photograph of everybody in his family, going back many, many years. Right at the beginning are the photographs of all his great-great-grandparents. How many photographs are in this section of the album?
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Old Farmer Palmer has a herd of cows, but he always seems to forget how many animals there are. When he counts them he just makes sure he can see 6 cows from each window of his house:
One night, however, Russell the Rustler took away half of the herd. Farmer Palmer didn't notice for ages because the next morning he could still see 6 cows from each window. How was it done?
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One afternoon, Hungry Horace made a large number of mince pies for his Christmas party the following day. He left them to cool overnight.
During the night Horace's brother Boris came downstairs and divided the mince pies into four equal piles with one left over, which he ate. He also ate one of the four piles, then went back to bed.
Later on, Horace's sister Doris came downstairs and again divided the mince pies into four equal piles with one left over, which she ate. She also ate one of her four piles and returned to bed.
In the morning, Horace found 60 pies left. How many had he made?
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It gets a bit chilly up in the North Pole, and recently Father Christmas caught a cold. Fortunately, he did manage to get a message through via one of his elves. Unfortunately, the naughty elf has hidden the message in a mysterious code. Can you crack it?
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No. 2: "A Weighty Problem"
Three possible answers:
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No. 3: "Knight Walk"
No. 4: "The Great Domino
Cover-Up"
Well, how unfair can I be? It was impossible! Those who read the puzzle carefully would have seen my little clue at the bottom, but it seems nobody took the hint. I think I am in for a rough time from all those people who spent hours trying to work it out....
Why It Can't Be Done
The chess board in the puzzle certainly had 62 squares, but if you were observant you would have seen that I removed two WHITE squares, leaving 32 blacks and only 30 whites.
Each domino covers exactly one white and one black square. So you'll always have two blacks left over!
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No. 5: "The OXO Game"
The trick in each of the four cases is to make a second move in a cell which creates TWO lines for O to block at once!
No. 6: "The Make-You-Very-Cross
Number"
Thirty minims normally cost 60p.
So minims are 2p each.
"Ten minims and five crotchets" is then "20p and five crotchets".
If this is normally 40p then five crotchets must normally cost 20p.
So crotchets are 4p each.
Similarly "Ten crotchets and ten quavers" is "40p and ten quavers".
If this normally costs £1.20 then ten quavers must normally cost 80p.
So quavers are 8p each.
The total full price of one minim, one crotchet and one quaver is then 2 + 4 + 8 = 14p
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No. 9: "A Hole New Board Game"
No. 10: "Match(es) Of The Day"
Note that there are four small squares and four small triangles. Can you also see the large square and the two large triangles?
No. 11: "Ancestrally Speaking"
1 Hungry Horace
2 parents
4 grandparents
8 great-grandparents
16 great-great-grandparents
No. 12: "(Of Course I've) Herd Of
Cows"
Many solutions and variations are possible once you get the idea! Here's one simple version:
HORACE MADE 109 MINCE PIES
During the night Boris made four piles of 27 and ate the extra one. He then ate one of the piles. (Total: 28 eaten)
Later Doris divided the remaining 81 pies into four piles of 20 and ate the extra one. She then ate one of the piles.
(Total: 21 eaten)
In the morning Horace found 60 left!
Keep trying!!
Stephen Froggatt February 2000