Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 139 · 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.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 211 (c) 212 (d) 210
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 11 (c) 10 (d) 7
3. 3.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
5. 5.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 298 (c) 339 (d) 340
6. 6.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) 57 (b) 54 (c) 18 (d) 162
7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 4 (b) 16 (c) 14 (d) 15
8. 8.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 9 (b) 30 (c) 81 (d) 27
9. 9.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 642 (b) 643 (c) 633 (d) 500
10. 10.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) 45 (b) 18 (c) 5 (d) 15
11. 11.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 116 (c) 125 (d) 126
12. 12.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) 16 (b) 144 (c) 48 (d) 51
13. 13.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 303 (c) 280 (d) 312
14. 14.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 42 (c) 34 (d) 24
15. 15.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) 33 (b) 90 (c) 10 (d) 30
16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 16 (d) 18
17. 17.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 288 (c) 297 (d) 298
18. 18.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
19. 19.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 5 (d) 15
21. 21.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
22. 22.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 66 (c) 198 (d) 22
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.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) 6 (d) 18
25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 5 (d) 3
27. 27.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) 45 (c) 15 (d) 48
28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 1 (d) 4
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 3 (c) 4 (d) 2
30. 30.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 430 (c) 429 (d) 420
31. 31.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 7 (b) 9 (c) 6 (d) 8
33. 33.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 104 (c) 86 (d) 96
34. 34.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
35. 35.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 19 (c) 60 (d) 57
36. 36.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 472 (d) 601
37. 37.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 126 (c) 14 (d) 45
38. 38.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 600 (c) 478 (d) 610
39. 39.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 160 (d) 159
40. 40.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6

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