Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 658 · 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 76? (a) 7 (b) 19 (c) 17 (d) 18
2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 3 (b) 5 (c) 6 (d) 4
3. 3.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 570 (c) 452 (d) 571
4. 4.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 422 (b) 526 (c) 525 (d) 516
5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 18 (c) 6 (d) 17
6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 16 (d) 14
8. 8.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 373 (b) 372 (c) 320 (d) 363
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 68? (a) 7 (b) 5 (c) 8 (d) 6
10. 10.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 259 (d) 258
11. 11.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
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) 33 (b) 10 (c) 90 (d) 30
13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 3 (d) 4
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 17 (d) 19
15. 15.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 39 (c) 12 (d) 36
16. 16.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) 6 (b) 18 (c) 21 (d) 54
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 19 (d) 20
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) 69 (b) 23 (c) 72 (d) 207
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 1 (d) 2
20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 15 (b) 17 (c) 7 (d) 16
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 52? (a) 15 (b) 17 (c) 5 (d) 16
22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 18 (d) 7
23. 23.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) 36 (b) 99 (c) 33 (d) 11
24. 24.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
25. 25.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
26. 26.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 405 (c) 415 (d) 414
27. 27.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 556 (b) 546 (c) 555 (d) 442
28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 17 (d) 16
30. 30.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 316 (c) 282 (d) 315
31. 31.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 464 (c) 589 (d) 588
32. 32.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) 24 (c) 7 (d) 21
33. 33.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) 54 (c) 162 (d) 18
34. 34.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 5 (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 44? (a) 4 (b) 2 (c) 3 (d) 5
37. 37.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 345 (b) 336 (c) 302 (d) 346
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 19 (b) 21 (c) 9 (d) 20
39. 39.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
40. 40.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) 210 (c) 207 (d) 208

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