ACROSS
2. A power of two (4)
5. A prime factor of 12345 (3)
6. Six more than a multiple of 13 ACROSS (3)
8. A cube (2)
10. The product of the digits of 25 ACROSS and also less than half of 23 ACROSS (2)
11. The mean of 4 DOWN, 8 ACROSS, 10 ACROSS, 13 ACROSS and 20 ACROSS and more than 3 DOWN (2)
13. A Fibonacci number (2)
14. A multiple of seven (3)
17. Eight less than a square (3)
19. Seven less than 26 DOWN (2)
20. A number that is greater than 3 DOWN and less than 27 DOWN (2)
22. An even number that is the sum of a square and a triangular number in two different ways (2)
23. A prime whose digits add up to five (2)
25. A square and a multiple of five (3)
28. A multiple of 14 that includes a two and an eight among its digits (3)
29. Nine more than a power of 20 ACROSS (4)
DOWN
1. One hundred and ninety-five less than a square (4)
2. One less than a Fibonacci number (3)
3. The highest common factor of 9 DOWN and 15 DOWN (2)
4. The sum of two powers of two (2)
6. (25 ACROSS) per cent of 24 DOWN (3)
7. The shortest side of a right-angled triangle whose longer sides are 24 DOWN and 25 ACROSS (3)
9. The square of a triangular number; also one less than a multiple of five (3)
12. A factor of 732, each of whose digits is a power of two (3)
15. Five multiplied by 3 DOWN (3)
16. An even square; also a multiple of 8 ACROSS (3)
17. A multiple of 17, the product of whose digits is a square multiplied by seven (3)
18. A multiple of nine (3)
21. A power of 21 (4)
24. A factor of 360 (3)
26. Seven more than 19 ACROSS (2)
27. A cube (2)
113. How many routes?
How many different routes are there from S to T that do not go through either of the points U and V more than once?
114. What Rachel drinks
A bottle contains 750 ml of mineral water. Rachel drinks 50% more than Ross, and these two friends finish the bottle between them.
How much does Rachel drink?
115. A magic product square
Place the numbers
in the squares of the grid, with one number in each square, so that the products of the numbers in the three rows, the three columns and the two diagonals are all equal to 1.
116. What is the angle?
The diagram shows a regular hexagon PQRSTU, a square PUWX and an equilateral triangle UVW.
What is the size of angle TVU?
117. A sum of numbers
Consider the list of all four-digit numbers that can be formed using only the digits 1, 2, 3 and 4, with no repetitions.
What is the sum of all the numbers in this list?
118. How many knights?
A group of 25 people consists of knights, serfs and damsels.
Each knight always tells the truth, each serf always lies, and each damsel alternates between telling the truth and lying.
When each of them was asked: ‘Are you a knight?’, 17 of them said ‘Yes’. When each of them was then asked: ‘Are you a damsel?’, 12 of them said ‘Yes’. When each of them was then asked: ‘Are you a serf?’, 8 of them said ‘Yes’.
How many knights are in the group?
119. Crossing the river
Two adults and two children wish to cross a river. They make a raft, but it will carry only the weight of one adult or two children.
What is the minimum number of times the raft must cross the river to get all four people to the other side?
(Note: The raft may not cross the river without at least one person on board.)
120. Gluing cubes
A cube is made by gluing together a number of unit cubes face-to-face. The number of unit cubes that are glued to exactly four other unit cubes is 96.
How many unit cubes are glued to exactly five other unit cubes?
121. Mr Gallop’s ponies
Mr Gallop has two stables that each initially housed three ponies. His prize pony, Rein Beau, is worth £250 000. Rein Beau usually spends his day in the small stable, but when he wandered across into the large stable, Mr Gallop was surprised to find that the average value of the ponies in each stable rose by £10 000.
What is the total value of all six ponies?
122. Making a square
I have two types of square tile. One type has a side length of 1 cm and the other has a side length of 2 cm.
What is the smallest square that can be made with equal numbers of each type of tile?