Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 721 · 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 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 19 (d) 20
2. 2.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 477 (c) 486 (d) 396
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
4. 4.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) 8 (b) 24 (c) 27 (d) 72
5. 5.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
6. 6.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 6 (b) 16 (c) 17 (d) 18
8. 8.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 9 (b) 6 (c) 8 (d) 7
10. 10.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
11. 11.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
12. 12.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) 162 (c) 54 (d) 18
13. 13.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 60 (c) 63 (d) 20
14. 14.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) 5 (c) 15 (d) 18
15. 15.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 4 (d) 17
16. 16.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 229 (c) 224 (d) 219
17. 17.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 186 (c) 194 (d) 176
18. 18.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) 171 (c) 57 (d) 19
19. 19.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 208 (c) 210 (d) 207
20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 2 (b) 4 (c) 5 (d) 3
21. 21.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 136 (c) 135 (d) 126
22. 22.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 526 (c) 516 (d) 422
23. 23.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 280 (c) 313 (d) 312
24. 24.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
25. 25.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 400 (b) 483 (c) 492 (d) 493
26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 7 (b) 5 (c) 8 (d) 4
27. 27.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) 63 (b) 21 (c) 24 (d) 7
28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 7 (d) 19
29. 29.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
30. 30.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 522 (c) 531 (d) 532
31. 31.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) 30 (c) 90 (d) 10
32. 32.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
33. 33.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 384 (c) 393 (d) 394
34. 34.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 136 (c) 128 (d) 127
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 16
36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 3 (b) 2 (c) 5 (d) 4
37. 37.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 81 (d) 90
38. 38.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) 51 (b) 16 (c) 48 (d) 144
39. 39.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 15 (d) 16

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