JMC 2017 Challenge cont.

16. In New Threeland there are three types of coins: the 2p; the 5p; and one other.

The smallest number of coins needed to make 13p is three.

The smallest number of coins needed to make 19p is three.

What is the value of the third type of coin?

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17. I add up all even numbers between 1 and 101. Then from my total I subtract all odd numbers between 0 and 100.

What is the result?

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18. What is the sum of the digits in the completed crossnumber?

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19. The diagram shows a regular hexagon PQRSTU, a square PUWX and an equilateral triangle UVW.

What is the angle TVU ?

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20. The range of a list of integers is 20, and the median is 17.   What is the smallest possible number of integers in the list?

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21. The small trapezium on the right has three equal sides and angles of 60° and 120°. Nine copies of this trapezium can be placed together to make a larger version of it, as shown.

The larger trapezium has perimeter 18 cm. What is the perimeter of the smaller trapezium?

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22. In the window of Bradley's Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles.

How many unicycles are in the window?

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23. The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer.

Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark.

How many cells have more than 1 mark?

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24. A large solid cube is cut into two pieces by a single plane cut. How many of the following four shapes could be the shape of the cross-section formed by the cut?

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25. The distance between Exeter and London is 175 miles. Sam left Exeter at 10:00 on Tuesday for London. Morgan left London for Exeter at 13:00 the same day. They travelled on the same road. Up to the time when they met, Sam's average speed was 25 miles per hour, and Morgan's average speed was 35 miles an hour.

At what time did Sam and Morgan meet?

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