Clock Arithmetic and Number Theory - November 2003, Stage 2&3

Problems

problem icon

Trebling

Stage: 2 Challenge Level: Challenge Level:1

Can you replace the letters with numbers? Is there only one solution in each case?

problem icon

The Deca Tree

Stage: 2 Challenge Level: Challenge Level:1

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

problem icon

A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

problem icon

Adding Plus

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

problem icon

Clocked

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

problem icon

Lastly - Well

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What are the last two digits of 2^(2^2003)?

problem icon

What an Odd Fact(or)

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?

problem icon

John's Train Is on Time

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

problem icon

Excel Investigation: the Difference of Two (same) Powers

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

If you take two integers and look at the difference between the square of each value, there is a nice relationship between the original numbers and that difference. Can you find the pattern using. . . .