Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 899 · 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 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) 18 (b) 15 (c) 5 (d) 45
2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 18 (d) 8
3. 3.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 411 (c) 352 (d) 420
4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 16 (d) 15
5. 5.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 5 (b) 6 (c) 4 (d) 7
8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
9. 9.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
10. 10.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) 39 (c) 13 (d) 42
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 14 (b) 4 (c) 16 (d) 15
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 10 (c) 13 (d) 7
13. 13.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 5 (c) 4 (d) 7
15. 15.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 279 (c) 280 (d) 270
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 8 (d) 18
17. 17.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
18. 18.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 625 (d) 624
19. 19.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) 6 (c) 21 (d) 18
20. 20.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 579 (d) 580
21. 21.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 271 (c) 261 (d) 270
22. 22.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 6 (d) 8
23. 23.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) 7 (b) 24 (c) 21 (d) 63
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 3 (b) 1 (c) 2 (d) 4
25. 25.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 161 (c) 170 (d) 152
26. 26.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) 72 (b) 23 (c) 69 (d) 207
27. 27.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) 185 (c) 176 (d) 186
28. 28.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 234 (c) 351 (d) 244
29. 29.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 643 (b) 642 (c) 500 (d) 633
30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 1 (b) 2 (c) 3 (d) 4
31. 31.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
32. 32.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 416 (c) 516 (d) 517
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 4 (d) 5
34. 34.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) 14 (b) 45 (c) 126 (d) 42
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 3 (d) 15
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 14 (c) 3 (d) 15
37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 8 (d) 17
38. 38.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 336 (c) 397 (d) 396
39. 39.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) 636 (c) 637 (d) 496
40. 40.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 126 (d) 125

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