Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 527 · 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.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 3 (b) 4 (c) 1 (d) 2
2. 2.The numbers 19 to 27 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) 207 (c) 72 (d) 23
3. 3.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
4. 4.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
5. 5.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 117 (b) 13 (c) 42 (d) 39
6. 6.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 370 (c) 360 (d) 318
7. 7.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
8. 8.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) 18 (c) 54 (d) 162
9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
10. 10.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 476 (b) 607 (c) 597 (d) 606
11. 11.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 7 (c) 24 (d) 63
12. 12.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 228 (c) 229 (d) 224
13. 13.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
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) 33 (b) 36 (c) 99 (d) 11
15. 15.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) 27 (c) 30 (d) 81
16. 16.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) 17 (b) 153 (c) 54 (d) 51
17. 17.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
18. 18.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 310 (c) 309 (d) 278
19. 19.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
20. 20.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
21. 21.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) 75 (b) 216 (c) 72 (d) 24
22. 22.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) 57 (b) 60 (c) 19 (d) 171
23. 23.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 162 (c) 153 (d) 154
24. 24.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) 297 (c) 298 (d) 288
25. 25.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 6 (c) 8 (d) 10
26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 19 (b) 17 (c) 8 (d) 18
27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 15 (b) 17 (c) 5 (d) 16
28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 19 (d) 18
29. 29.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 6 (b) 5 (c) 3 (d) 4
31. 31.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) 15 (b) 5 (c) 18 (d) 45
32. 32.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 628 (d) 627
33. 33.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 198 (d) 207
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 16 (d) 17
35. 35.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 446 (c) 552 (d) 561
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 18 (b) 17 (c) 7 (d) 19
37. 37.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 496 (c) 402 (d) 486
38. 38.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
39. 39.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 316 (c) 315 (d) 306
40. 40.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 452 (b) 570 (c) 571 (d) 561

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