The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind. Литагент HarperCollins USD

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       ACROSS

       1. A prime factor of 8765 (4)

       4. The interior angle, in degrees, of a regular polygon; its digits have a product of 12 (3)

       6. A Fibonacci number whose digits add up to twenty-four (3)

       7. A prime that is one greater than a square (2)

       8. Ninety-nine greater than the number formed by reversing the order of its digits (3)

      10. A multiple of 25 ACROSS (3)

      12. 9 DOWN multiplied by seven (3)

      15. A number with seven factors (2)

      17. The third side of a right-angled triangle with hypotenuse 9 DOWN and other side 25 ACROSS (2)

      19. (10 ACROSS) per cent of 8 ACROSS (3)

      21. An odd multiple of nine (3)

      23. The product of the seventh prime and the eleventh prime (3)

      25. An even number (2)

      26. The lowest common multiple of 25 ACROSS and 11 DOWN (3)

      28. A multiple of eleven, and also the mean of 12 ACROSS, 16 DOWN, 19 ACROSS, 24 DOWN and 27 DOWN (3)

      29. A power of nineteen (4)

       DOWN

       2. An even square (3)

       3. One third of 21 ACROSS (2)

       4. The interior angle, in degrees, of the regular polygon that has twice as many sides as the regular polygon whose interior angle, in degrees, is 4 ACROSS (3)

       5. One less than a multiple of eleven (3)

       8. A power of nine (4)

       9. The mean of 3 DOWN, 7 ACROSS, 13 DOWN, 17 ACROSS and 27 DOWN (2)

      11. Ninety-one less than 10 ACROSS (2)

      13. The sum of the squares of the digits of 23 ACROSS (2)

      14. A factor of 4567 (4)

      16. The difference between 11 DOWN and 3 DOWN (2)

      18. The square root of 8 DOWN (2)

      20. The highest common factor of 10 ACROSS and 24 DOWN (2)

      21. The total number of days in a year in the months whose names do not contain the letter A (3)

      22. A prime that is ten less than a cube (3)

      24. A square multiplied by five; the product of its digits is 40 (3)

      27. A triangular number that is the sum of two prime numbers that differ by eight (2)

       [SOLUTION]

Week 25

      169. Non-factors of 720

      Sam starts to list in ascending order every positive integer that is not a factor of 720.

      Which is the tenth number in her list?

       [SOLUTION]

      170. What size is JMO?

      In the diagram, JK and ML are parallel. JK = KO = OJ = OM and LM = LO = LK.

      Find the size of the angle JMO.

       [SOLUTION]

      171. Amrita’s numbers

      Amrita has written down four whole numbers. If she chooses three of her numbers at a time and adds up each triple, she obtains totals of 115, 153, 169 and 181.

      What is the largest of Amrita’s numbers?

       [SOLUTION]

      172. Where do the children come from?

      Five children, boys Vince, Will and Zac, and girls Xenia and Yvonne, sit at a round table. They come from five different cities: Aberdeen, Belfast, Cardiff, Durham and Edinburgh. The child from Aberdeen sits between Zac and the child from Edinburgh. Neither of the two girls is sitting next to Will. Vince sits between Yvonne and the child from Durham. Zac writes to the child from Cardiff.

      Where does each child come from?

       [SOLUTION]

      173. Find four integers

      Find four integers whose sum is 400 and such that the first integer is equal to twice the second integer, three times the third integer and four times the fourth integer.

       [SOLUTION]

      174. Bradley’s Bicycle Bazaar

      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?

       [SOLUTION]

      175. Liz and Mary’s problems

      Liz and Mary compete in solving problems. Each of them is given the same list of 100 problems. For any problem, the first of them to solve it gets 4 points, while the second to solve it gets 1 point. Liz solved 60 problems, and Mary also solved 60 problems. Together, they got 312 points.

      How many problems were solved by both of them?

       [SOLUTION]

Week 26

      176. Edinburgh to London

      Travelling by train from Edinburgh to London, I passed a sign saying ‘London 150 miles’. After seven more miles, I passed another sign saying ‘Edinburgh 250 miles’.

      How far is it by train from Edinburgh to London?

       [SOLUTION]