Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 138 · 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 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) 81 (d) 30
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 5 (d) 3
3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 15 (c) 14 (d) 4
4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
5. 5.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 151 (c) 142 (d) 152
6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
7. 7.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 291 (c) 282 (d) 266
8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 2 (d) 3
10. 10.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 204 (c) 199 (d) 198
11. 11.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
12. 12.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) 33 (c) 90 (d) 30
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 15 (b) 16 (c) 5 (d) 17
14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 8 (d) 20
15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 17 (c) 15 (d) 16
16. 16.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) 24 (d) 34
17. 17.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 77 (c) 68 (d) 86
18. 18.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) 207 (b) 72 (c) 69 (d) 23
19. 19.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) 229 (c) 224 (d) 228
20. 20.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 102 (c) 94 (d) 93
21. 21.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 597 (c) 607 (d) 476
22. 22.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
23. 23.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 66 (d) 57
24. 24.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
25. 25.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) 72 (b) 216 (c) 24 (d) 75
26. 26.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 35 (d) 26
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 18 (d) 7
28. 28.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
29. 29.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) 72 (b) 8 (c) 24 (d) 27
30. 30.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 255 (c) 256 (d) 242
31. 31.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 324 (c) 333 (d) 294
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 4 (d) 1
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
34. 34.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) 63 (b) 66 (c) 189 (d) 21
35. 35.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 636 (d) 496
36. 36.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) 60 (b) 19 (c) 57 (d) 171
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 4 (d) 16
38. 38.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 112 (c) 130 (d) 122
39. 39.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) 22 (d) 198
40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 19 (b) 20 (c) 21 (d) 9

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