Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 764 · 40 questions

How to solve it (Count place by place): Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice). Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

1. 1.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 144 (c) 16 (d) 51
2. 2.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 21 (c) 18 (d) 6
3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 9 (b) 21 (c) 19 (d) 20
4. 4.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 115 (c) 106 (d) 116
5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 6 (b) 8 (c) 7 (d) 9
6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 7 (d) 18
7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 3 (c) 2 (d) 1
8. 8.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 24 (b) 27 (c) 72 (d) 8
9. 9.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 131 (c) 140 (d) 122
10. 10.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 16 (b) 17 (c) 18 (d) 7
12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 6 (d) 4
13. 13.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 72 (d) 24
14. 14.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 11 (b) 33 (c) 36 (d) 99
15. 15.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 272 (b) 291 (c) 301 (d) 300
16. 16.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 5 (c) 15 (d) 45
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 3 (d) 4
18. 18.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 417 (c) 408 (d) 350
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 5 (d) 4
20. 20.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 204 (c) 208 (d) 195
21. 21.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 135 (b) 15 (c) 45 (d) 48
22. 22.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 90 (c) 33 (d) 30
23. 23.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 54 (c) 153 (d) 17
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 6 (b) 8 (c) 5 (d) 7
25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 4 (b) 3 (c) 2 (d) 1
26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 16 (c) 15 (d) 5
27. 27.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 63 (d) 66
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
29. 29.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 176 (c) 158 (d) 167
30. 30.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 428 (c) 525 (d) 535
31. 31.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
33. 33.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 397 (c) 336 (d) 396
34. 34.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 12 (d) 39
35. 35.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
36. 36.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 18 (c) 57 (d) 162
37. 37.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 185 (c) 194 (d) 186
38. 38.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
39. 39.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
40. 40.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 93 (c) 94 (d) 84

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