Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 473 · 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 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 322 (c) 312 (d) 321
2. 2.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) 153 (b) 54 (c) 51 (d) 17
3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 5 (d) 7
4. 4.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) 23 (b) 72 (c) 69 (d) 207
5. 5.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 102 (c) 120 (d) 111
6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 14 (b) 16 (c) 5 (d) 15
8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 18 (d) 16
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 20 (d) 8
10. 10.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 340 (c) 402 (d) 403
11. 11.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 11 (c) 13 (d) 14
13. 13.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
14. 14.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
16. 16.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) 22 (c) 66 (d) 198
17. 17.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 538 (b) 537 (c) 430 (d) 528
18. 18.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) 72 (c) 24 (d) 216
19. 19.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 11 (d) 8
20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 6 (d) 4
21. 21.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) 408 (c) 417 (d) 350
22. 22.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) 27 (d) 81
23. 23.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
24. 24.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) 99 (b) 33 (c) 11 (d) 36
25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 14 (b) 15 (c) 4 (d) 16
26. 26.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
27. 27.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 4 (b) 7 (c) 6 (d) 5
29. 29.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) 20 (b) 63 (c) 60 (d) 180
30. 30.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
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 15 (b) 3 (c) 14 (d) 13
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 17 (d) 18
33. 33.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 169 (c) 178 (d) 170
34. 34.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 31 (c) 40 (d) 32
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) 561 (c) 446 (d) 552
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) 57 (b) 162 (c) 18 (d) 54
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) 194 (b) 176 (c) 185 (d) 186
38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 6 (c) 7 (d) 5
39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 3 (b) 5 (c) 2 (d) 4
40. 40.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 310 (c) 357 (d) 348

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