Community Primary School

*The Weekly Puzzle is taking a break. Well done to the winners of Puzzles 6a and 6b set over half-term.*

**Puzzle #6a - Puzzler of the Week - Kyle Nelson (Y3)**

**Q6a. In this addition, G, N and O represent different digits, none of which is zero. What are the numbers in this sum?**

Solution

**O = 2, N = 3 and G = 9, making the sum 23+23+23+23=96.**

**Puzzle #6b - Puzzler of the Week - Lyla Milnes (Y2)**

**Q6b. A number lock has a 3-digit code. Can you crack the code using the clues?**

Solution

**The answer is 052.**

Clue 4 tells you none of 7, 3 or 8 are possible.

Clue 5 tells you one of 7, 8 or 0 is a correct digit. It therefore must be 0, albeit not in the third position.

Clue 3 tells you two of 2, 0 or 6 are correct but in the wrong positions. As you know 0 is correct from clue 5, 0 must therefore be in the first position. **0** so far**

Clue 1 and 2 tells you one number is correct in both, but it's position is correct in clue 1 and incorrect in clue 2. Therefore 6 cannot be the correct digit since it is in the same position in both clues.

Clue 3 can now be used to deduce 2 is another digit in the code, and clue 1 tells us it must be in the third position. **0*2 so far**

The missing digit is in the second position. Clue 2 tells us the missing digit is either 4 or 5 (having already discounted 6). 4 is currently in the second position but the clue tells us the missing digit is not yet in the correct position. We can deduce therefore that 5 must be the missing digit. **052**

**Puzzle #5 - Puzzler of the Week - Ebony Hitchen (Y4)**

**Q. In this partly completed pyramid, each rectangle is to be filled with the sum of the two numbers in the rectangles immediately below it.**

**What number should go in the red rectangle?**

**(There's no trick here - only maths!)**

Solution

**The answer is 3.**

From top to bottom: 105; **58**, 47; 31, **27**, **20**; **17**, **14**, 13, **7**; **12**, **5**, 9, 4, **3**

**Q. In the sum below, the digits have been replaced by shapes. Identical shapes have the same value. What is the value of the square?**

Solution

**The answer is 6.**

The sum consists of an unknown value of ones + the same unknown value of ones + an unknown values of tens and ones, resulting in an unknown value of hundreds, tens and ones. With each digit in the result being identical, the highest possible result when adding the described values is 111. Using similar logic, the only possible value of the circles is 99. Once you have realised this, you can calculate the value of the square by inverse operation:

111 = 99 + 2 squares, so 2 squares = 12, and so 1 square = 6

A tricky puzzle, the hardest one yet. Well done if you got the correct answer.

**Q. The matchsticks in the picture are arranged to form a number sentence in Roman numerals, but obviously six minus four is not nine. Which matchstick (labelled 1 to 12) would you need to move in order to make the number sentence correct?**

*Image taken from parallel.org.uk - older pupils may wish to check out this great (challenging!) maths activity site.*

Solution

Move matchstick 3 so that it crosses matchstick 4 to make a plus sign. Then we have 5 + 4 = 9.

**In the image below, what is the number of the parking space taken by the car?**

Solution

An easy one if you spotted the picture was upside-down! The answer is 87, because if you look it at from the driver's point of view, then the numbers read 86 (not 98), 87, 88, 89, 90, 91 (not 16).

**The diagram below shows a rectangle placed on a grid of 1 cm × 1 cm squares.**

**What is the area of the rectangle in cm**^{2}**?**

Solution

The total area of the 8 × 8 grid in cm^{2} is 8^{2} = 64.

The two larger triangles in the top left and bottom right corners of the grid make up a 5 × 5 square with area 25 cm^{2}.

The two smaller triangles in the other corners of the grid make up a 3 × 3 square with area 9 cm^{2}.

So the area of the rectangle, in cm^{2}, 64 - 25 - 9 = 30.

Each week we will publish a new puzzle or problem for you to solve. The puzzles won't always have a maths theme: sometimes you'll be faced with word or picture problems.

You're welcome to get help from friends and family, or use the internet to help. Once you have worked out the answer, fill in the form below with your answer, name and class.

One winner will be randomly drawn from all entries received and they will be presented with a certificate in assembly at the end of the week.

You can only submit your answer once - multiple entries will be removed from the draw.

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Our school website design and school mobile apps are created with School Jotter, a Webanywhere product. [Administer Site]