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The Ultimate Mathematical Challenge: Over 365 puzzles to test your wits and excite your mind
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A regular octagon is placed inside a square, as shown.
The shaded square connects the midpoints of four sides of the octagon.
What fraction of the outer square is shaded?
[SOLUTION] (#litres_trial_promo)
137. ODD plus ODD is EVEN
Find all possible solutions to the ‘word sum’ shown.
Each letter stands for one of the digits 0−9 and has the same meaning each time it occurs. Different letters stand for different digits. No number starts with a zero.
[SOLUTION] (#litres_trial_promo)
138. Only odd digits
How many three-digit multiples of 9 consist only of odd digits?
[SOLUTION] (#litres_trial_promo)
139. How many tests?
Before the last of a series of tests, Sam calculated that a mark of 17 would enable her to average 80 over the series, but that a mark of 92 would raise her average mark over the series to 85.
How many tests were in the series?
[SOLUTION] (#litres_trial_promo)
140. Three primes
Find all positive integers p such that p, p + 8 and p + 16 are all prime.
[SOLUTION] (#litres_trial_promo)
Crossnumber 5 (#ulink_6f4f13ad-e843-5f09-a109-9e98fe449e11)
ACROSS
1. The cube of a square (5)
4. Eight less than 5 DOWN (3)
6. One less than a multiple of seven (3)
7. A prime factor of 20 902 (4)
10. A number whose digits successively decrease by one (3)
12. Sixty per cent of 20 DOWN (3)
14. A multiple of seven (3)
15. A multiple of three whose digits have an even sum (3)
16. The square of a square (3)
17. A prime that is one less than a multiple of six (3)
19. Eleven more than a cube (4)
22. A number all of whose digits are the same (3)
24. A number that leaves a remainder of eleven when divided by thirteen (3)
25. The square of a prime; the sum of the digits of this square is ten (5)
DOWN
1. A number with an odd number of factors (3)
2. Four less than a triangular number (3)
3. The square root of 9 DOWN (2)
4. A factor of 12 ACROSS (3)
5. The longest side of a right-angled triangle whose shorter sides are 3 DOWN and 4 ACROSS (3)
8. A Fibonacci number (5)
9. The square of 3 DOWN (4)
11. Three more than an even cube (5)
13. A prime factor of 34567 (4)
17. The mean of 10 ACROSS, 16 ACROSS, 18 DOWN, 20 DOWN and 21 DOWN (3)
18. A power of eighteen (3)
20. Two less than 22 ACROSS (3)
21. A number whose digits are those of 12 ACROSS reversed (3)
23. A multiple of twenty-three (2)
[SOLUTION] (#litres_trial_promo)
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Последний отзыв
Книга дельная. Без воды, приводятся реальные кейсы и способы их разрешения. Много практичных полезных советов и методик. Кое-что уже испробовала в дел...
Далее