### Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Tea Cups

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

### Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

# Birthday Cake Candles

##### Age 7 to 11Challenge Level

We had a number of solutions sent in from the Peak School in Hong Kong:

Victoria K and F wrote...

Lasting one year:
1st   2nd   3rd   4th   5th   6th   7th   8th   9th   10th   11th
1c     2c     2c     3c    4c    6c     7c    8c    9c     10c    11c     = 66 candles

Since the candles only last one year, Ben's parents will have to buy new candles every year.

Lasting longer than one year:
1st   2nd   3rd   4th   5th   6th   7th   8th   9th   10th   11th
1c     1c     1c     1c    1c    1c     1c    1c    1c     1c       1c    = 11 candles

Since the candles last longer than one year, Ben's parents will have to only buy one candle each year, since Ben gets one year older each year.

Similar solutions came from Anna and Alyssa, Zach, Haider, Nicholas, and Ian and Arthur.

We also had several solutions from Winns Primary School in London. Roxy wrote:

Ben's parents need to buy the amount of candles of his age. Every time they need to buy more. I wrote down the amount of candles each year until I got to 11 and then I counted them up and got 66, that is the answer. What if Ben was born on a leap year?

I think the answer is 66 because they have the same amount candles as the age that Ben is turning for 11 years straight. Therefore, you need to add all the numbers from 1 through 11. As it says including his 11th birthday. Now on to the what if question...

From my perspective, I think each candle lasts 2 yrs.

Also from the same school, we had solutions from Reece, Alex, Hester, Ayman, Samson, Jessie, Jathusha, Che and Hierthika.

We also received solutions from Joe, Ayobami, Hamsini, Ava, Zackary, Aoife, Sakina, Gracie, Millie and Niamh at Nene Valley Primary School. Jessica, Finlay and Suzanna sent in this picture:

Aarti from the International School Utrecht (ISU) in the Netherlands wrote:

To solve this problem I used my addition skills. I added the numbers, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, which equals to 66. For baby Ben's every birthday, his parents will need to get a number of candles that is the same number as baby Ben's age. And that is why I used addition to solve this problem.

Thank you, too, to Fraser and Lissa, Aarnavi, Sophi and Antek from Kingsfleet School in Felixstowe who also sent in solutions.

Many of your solutions included further questions for everyone to consider:

Ben asks "What if Ben ate one-and-a-half cakes (6 up) (double candles)?" ,"What if they went until he died(87)?",
Milena asks "What if the candles had to go up to Ben's 16th birthday?","What if the candles lasted 5 years?" , "What if Ben had a twin sister named Benny?"
Alex asks "What if Ben had an older brother called Jay and he was 7, surprisingly he was born on the exact same day and the exact same time and they had to buy candles for him too? How many candles would you need?"
Adam asks "What if Baby Ben had a big brother called Charlie who was born a day after, but at the same time and he was 5 years old on Baby Ben's birthday. How many more candles until his 16th birthday would their parents need to buy? Explain why."
Sara asks "What if baby Ben had a brother three years older than him and a sister two years younger than him?  How many candles would they need? What if Ben died at 9 years?"
Linna asks "What if baby Ben had a candle with his age on it?"
Aaron asks "What if Ben had a 13-year-old brother who was born on February 29 and all the candles in their house lasted for 1 year? What if Ben was a triplet?"
Blessing asks "What if the candles lasted up to five years? What if they last up to ten years? What if Ben had a twin?"
Ben asks "What if Ben was born on a leap year?
Syd asks "What if Ben is one of a triplet?