Maths Challenges• Year 7 and 8

– 21st September– 28th September– 5th October– 12th October– 19th October– 9th November– 16th November– 30th November– 7th December

• Years 9,10,11– 21st September– 28th September– 5th October– 12th October– 19th October– 9th November– 16th November– 30th November– 7th December

The building company Baffle Batty have built a new cinema that has exactly 100 seats. Show how it is possible to sell exactly 100 tickets and make exactly £100 if the prices are:

Adults £10Children 10pPensioners 50p

A zoo contains only birds and rabbits. There are sixteen

heads and thirty-eight feet. How many birds are there in

the cage?

Pairs of identical rectangular strips, each measuring 3 by 1, are overlapped in a number of different ways to form three different shapes, shown in the diagram below. Which shape has the greatest perimeter?

A boy writes down the numbers from 1 to 20 in order and he notes that he has actually written down thirty-one digits in total.

If his list went from 1 to 1000 how many digits would he have written down?

If one-thousand digits were written down in total, how many complete numbers would have been written down?

Two sand timers have been designed to measure 9 minutes and 13 minutes respectively.

How would you use them to measure 30 minutes?

187

190 211

What number should replace the symbol?

In a test Amy scores

33 more points than

Danielle and Danielle

Scores 26 less than

James. Craig scores 16

more points than Fiona

and James scores 5

more than Craig.

Danielle and Craig

score 71 points

between them. How

many points do the

five people score in

total?

If I said that in three days' time it

would be a Thursday, I am sure that

most of you would have no difficulty

telling me that today was a Monday.

Try this one then. Yesterday was two

days before Monday. What day is it

today? Yes, you're right again. It's

Sunday. Do you get the idea?

Now let's tackle a similar question:

Three days ago, yesterday was the

day before Sunday. What day will it be

tomorrow?

Answer

How can I get the answer 24 by only using the numbers 8,8,3,3.

You can use add, subtract, multiply, divide, and brackets.

ALL the numbers must be used.

(Using square or cube roots may help)

Answers

Across1. Three times 19 down4. 19 down minus five6. 15 across plus eighty-three7. 17 across minus 28. 18 down plus thirty-eight10. 19 across minus sixty-six12. 3 down plus forty-seven14. 12 across doubled15. 13 down minus 15017. 20 down minus sixteen19. 5 down minus 13321. Minutes in four hours22. Four times 4 across23. Five times 10 down

Down1. 12 across divided by eleven2. 1 down plus twenty-five3. Minutes in three days4. Dozen in twelve gross5. Seconds in five minutes9. 17 down minus eleven10. 11 down minus eight11. Minutes in three hours13. 3 down divided by twelve16. 23 across doubled17. 14 across divided by eleven18. 4 down times three19. Months in nine years20. 3 down divided by six

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A car and a motorcycle set off from the same point to travel the same journey. The car has a start of four minutes before the motorcycle sets off. If the car travels at 80km/h and the motorcycle travels at 90km/h, how many kilometres will be travelled when the two vehicles are level?

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Use any numbers between 1 and 10 to fill the spaces. The rows, columns and diagonals must add up to the totals shown. Numbers can be repeated.

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A 15 N 9B 20 O 4C 7 P 10D 1 Q 17E 12 R 23F 24 S 13G 21 T 25H 14 U 3I 6 V 16J 19 W 11K 2 X 22L 8 Y 26M 18 Z 5

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This is a Nurikabe puzzle. The aim is to find out which squares should be shaded and which should be unshaded.

The numbers show how many squares are unshaded in the group that the number is present. The can be in any arrangement but cannot be connect diagonally.

Eventually all shaded squares must be connected.

A more complete set of rules can be found here.Show Answer

Father Christmas is delivering cards to houses numbered 1 to 100.  The price for each card is the same as the house number so, for example, house number 9 requires 9p in stamps, house number 38 needs 38p worth of stamps and of course, house number 39 needs 39p.  Unfortunately, Buddy the elf has run out of all the stamps except for 3p and 5p.  Which house numbers will get cards and which won't?

10cm20cm

5cm

Frugal Wrapping

What is the minimum amount of wrapping paper needed to wrap this box?

What about overlaps for sticking?

How much ribbon do you need?