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The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind
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107. How many lines?
The picture shows seven points and the connections between them.
What is the least number of connecting lines that could be added to the picture so that each of the seven points has the same number of connections with other points?
(Connecting lines are allowed to cross each other.)
[SOLUTION] (#litres_trial_promo)
108. Where in the list?
There are 120 different ways of arranging the letters U, K, M, I and C. All of these arrangements are listed in dictionary order, starting with CIKMU.
Which position in the list does UKIMC occupy?
[SOLUTION] (#litres_trial_promo)
109. Eva’s sport
Two sportsmen (Ben and Filip) and two sportswomen (Eva and Andrea) − a speed skater, a skier, a hockey player and a snowboarder − had dinner at a square table, with one person on each edge of the square.
The skier sat at Andrea’s left hand.
The speed skater sat opposite Ben.
Eva and Filip sat next to each other.
A woman sat at the hockey player’s left hand.
Which sport did Eva do?
[SOLUTION] (#litres_trial_promo)
110. Pedro’s numbers
Pedro writes down a list of six different positive integers, the largest of which is N. There is exactly one pair of these numbers for which the smaller number does not divide the larger.
What is the smallest possible value of N?
[SOLUTION] (#litres_trial_promo)
111. The speed of the train
A train travelling at constant speed takes five seconds to pass completely through a tunnel that is 85 m long, and eight seconds to pass completely through a second tunnel that is 160 m long.
What is the speed of the train?
[SOLUTION] (#litres_trial_promo)
112. What is ‘pqrst’?
The digits p, q, r, s and t are all different.
What is the smallest five-digit integer ‘pqrst’ that is divisible by 1, 2, 3, 4 and 5?
[SOLUTION] (#litres_trial_promo)
Crossnumber 4 (#ulink_65a487f9-458b-5223-977a-e327917da255)
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)
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