3. How many?

The jelly design

wouldneed 200

ice cubes4.

Enough blocks?

There are exactly

enough..

The jelly design

wouldneed 200

ice cubes4.

Enough blocks?

There are exactly

enough..

There are 57 coins in the chest. The puzzle can be solved by trial and improvement or using a table.

(In a table, patterns of repeating numbers are more obvious. A table of only multiples of 3 gets a solution

more quickly but the pattern is less obvious.)

Children could use their table to make up similar puzzles, e.g. “There were less than 100 soldiers. If

the soldiers lined up in threes or fours or fives or sixes, there was always one left over.” How many

soldiers?

Outside: 8, 12, 16, 20, 24, 28, 32, 36

Inside: 1, 4, 9, 16, 25, 36, 49, 64

Total: 9, 16, 25, 36, 49, 64, 81, 100

Shield count quiz

1. +4

Re-arranged the letters spell out THOR, the Norse god of Thunder.

Up to 6 x 6 arrays, there are more shields on the outside. For 7 x 7 arrays and larger, there are

more inside.

Rules and jobs

Eric: 1, 4, 7, 10, 13, 16, .... The rule is add 3

Eric is a fisherman.

Thora: 1, 2, 4, 8, 16, 32, ... The rule is double successive terms

Thora is a weaver.

Olaf: 1, 2.5, 4, 5.5, 6, 7.5, ... The rule is add 1.5

Olaf is a blacksmith.

Godrun: 1, -3, -7, -11, -15, -19, ... The rule is minus 4

Godrun is a market trader.

In a group of 8, Hal should be number 1 in the circle. He should be 3rd in the circle for a group of 33.

For a group of 40 he should stand in position 17.

By filling in the table ‘Hal’s place’, children should find a repeating pattern and a doubling pattern of

odd numbers which they can use to make predictions. The pattern is quite sophisticated, linking

odd numbers with binary numbers.

Pattern 1: You can make 8 arrangements with five 1 x 2 rectangles. The different numbers of

arrangements produce the Fibonacci series of numbers: (1), 1, 2, 3, 5, 8. 13, 21, ...

Pattern 2: The sixth stone will have 21 runes on it. The series of triangle numbers begins: 1, 3, 6, 10,

15, 21, 28, 36, 45, ....

Pattern 3: 21 is the lowest number that can be made with one (21), two (15 + 6) or three leaves

(10 + 10 + 1).

Pattern 4: 31/32 of the fifth flag will be yellow.

Pattern 5: 8 cubes.

Fiery stone quiz

1. R, 2. A, 3. V, 4. E, 5. N

It spells out RAVEN. Odin, the chief Norse god, had two ravens, Huginn (thought) and Muginn (memory).

These two birds kept him informed of what was going on in the world.

Astrid’s baby: D (means ‘wisdom’)

Grim: B (means ‘victory’)

There are 6 permutations possible, if one is wrong, at least one other will be as well.

4 runes gives 4! (24 permutations)

5 runes gives 5! (120 permutations)

6 runes gives 6! (720 permutations)

purple; red and yellow mixed makes orange; yellow and blue mixed makes green)

100 + 50 = 250, Blue: 100 + 15 + 10 = 125 and Purple: 100 + 5 + 5 = 110)

solutions of the previous seven puzzles.

What’s missing?

3. E and S (planets in order from the Sun) Note: Pluto has been demoted. 4. S and E (One, Two,

Three, ...) 5. F and S (ordinal numbers: first, second, third, ...) 6. M and J (months of the year).

Fenja: 9 apples. Egil: 3 Ingun: None. Pigs can’t talk. Gotthorn: 3 trips (you can’t make half a trip).

Thorolf: Because he was drawing a graph.

A carrot is worth three onions.

onion = 1

apple = 2

carrot = 3

pear = 4

cabbage = 10.

outside.”) It isn’t quite so easy. As Alice shows, there are overlapping squares of 2 x 2, 3 x 3,

and so on.

The answers is 204 (64 + 49 + 36 + 25 + 16 + 9 + 4 + 1)

To get to the correct solution, children will have to be systematic. One way is to draw out a series of

small chessboard grids and work through each methodically. Alternatively, children can use the shortcut

of working out how many, say, 2 x 2 squares there are in a row, and then multiplying it by the number

in a column, which in this case is 7 x 7.

TOP.

Pippa is the Emperor penguin second from the right in the sixth row.

Shanta wins the trip. Here’s why...

Before the final question the scores stand at 1 for Shanta and 0 for Brad. Polar bears are only native

to the North Pole (Arctic) and so Brad’s answer is wrong and he gets a minus point. The final scores

are: Shanta 3 and Brad -1.

Back puzzle

Mike is 10 metres from his start position.

Minus money

(1) C, (2) A, (3) D and (4) B

Have you got the right altitude?

4 / 9 / 0

8 / -19 / E

7 / -9 / T

6 / -17 / I

2 / 19 / P

5 / -6 / S

1 / 17 / 0

3 / 6 / P

The secret word is OPPOSITE.

Rockhopper: +7, -8, +8, -3, -7 = -3

Chinstrap: +10, -8, +8, -3, -7 = 0

Emperor: +3, -10, -8, +12, +2 = -1

Macaroni: -10, +5, +5, -1, -3 = -2

Adelie: +5, +1, -7, -3, -1 = -5

King: -10, +5, +3, +8, -10, = -4

(1) B (-3°C), (2) I (-2°C), (3) G (-7°C), (4) F (-17°C),

(5) O (-15°C), (6) O (34°C), (7) T

Note: the drop in temperature on Day 5 is calculated from the real temperature of Day 4

and not the apparent wind chilled perceived temperature.

The secret word is BIGFOOT.

Bigfoot is the supposed North American cousin of the Yeti.

PGoldie Coin lives on the fourth floor. By deduction you will have discovered where the others lived...

Floor 15: Robin Banks

Floor 14: Baz Brass

Floor 13: Penny Galore

Floor 12: Roger Ruby

Floor 11: Amy Diamond

Floor 10: Bill Notes

Floor 9: Lady Dosh

Floor 8: Mandy Money

Floor 7: Major Cash

Floor 6: Arthur Dough

Floor 5: Debby Card

Floor 4: Goldie Coin

Floor 3: Sarah Copper

Floor 2: Lotsa Bread

Floor 1: Sylvia Spoon

Number tic-tac-toe

Have a go...

£40.00 – £16.00 (discount) = £24.00

Bob paid the most.

£50.00 – £25.00 (discount) = £25.00

Icy golf

Naomi took 8 shots

Bailey took 4 shots

Patesh took 2 shots

Justin took 9 shots

The last forecast before 7.00 am will be at 6.53 am.

The intervals between forecasts are 15 minutes. Throughout the day forecasts will be broadcast

at 08 minutes, 23 minutes, 38 minutes and 53 minutes past the hour.

From the story you should have worked out all the

temperatures except for Friday noon (this isn’t given).

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The identical palette and brushes is the furthest on the right in the second row..

(A) translation (B) rotation (C) reflection

Sophie’s transformation quiz

1. (e), 2. (h), 3. (s), 4. (a) and 5. (p)

The word spelt out by correct answers is ‘shape’.

2. Missing lines

Completed drawings for D to F:

(The steps’ risers change from facing right to facing left.)

Penguin perspective The penguins are all the same size. You knew that didn’t you! It’s the perspective

floor which fools the eye.

Hidden Faces The student’s professor is upside-down. The girl’s chin is the grandmother’s nose.

**Pages 10 and 11****/Knight's puzzle
**The knight can make it in 11 moves. There are other, longer routes.

Remy investigates

11: one cycle 5,6 1,10 9,2 7,4 3,8 15: See below

23: one cycle 12,11 1,22 21,2 19,4 15,8 7,16 9,14 5,18 13,10 3,20 17,6

Children will recognise that each pair of numbers created by the rules sums to the number being cycled.

For able children this can be demonstrated and justified algebraically.

When the starting number is a prime number the cycle contains all the possible combinations of pairs of

numbers that sum to the starting number (with the exception of 17 – are there others?).

Other odd numbers may need more that one cycle to exhibit all the possible pairs. For example, 15 has

3 cycles of pairs:

For even numbers the pairs form loops rather than cycles. Usually, the separate loops are linked and

have a final pair which includes zero.

Remy’s cycle begins an investigation in which a variety of questions can provide some fruitful starting

points. For example children can categorise* the types of number which create cycles, loops and spurs.

**Pages 14 and 15 ****/Are you puzzled?
Brush count**

Augusta sold two paintings at £70.00 and five at £20.00.

The tenth painting will have 220 white cells.

For any n x n grid, excluding the centre red cell, there are an equal number of red and white cells.

So the number of white cells for an n x n grid is 1/2(n2-1).

Who stole the Haywain?

set from the bottom set you get the price of the milk jug. The prices of the other items (even the price

of the individual mugs) can be found in a similar way.

The teapot is £7.00, the 4 mugs are £5.00 (£1.25p each), the sugar bowl is £3.00, the milk jug is £3.50

and the cake stand is £4.00.

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