Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 608 · 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 two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 17 (d) 15
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) 452 (c) 570 (d) 571
4. 4.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) 21 (b) 24 (c) 7 (d) 63
5. 5.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) 198 (d) 66
6. 6.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 165 (c) 174 (d) 166
7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 11 (c) 9 (d) 8
8. 8.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) 18 (b) 162 (c) 57 (d) 54
9. 9.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) 48 (b) 135 (c) 45 (d) 15
10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 18 (c) 17 (d) 7
14. 14.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
15. 15.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) 48 (c) 144 (d) 16
16. 16.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 264 (c) 289 (d) 288
17. 17.A book has 160 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 320 (c) 373 (d) 363
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 8 (b) 11 (c) 9 (d) 10
19. 19.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 235 (c) 225 (d) 234
20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 5 (b) 4 (c) 2 (d) 3
21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 16 (d) 15
22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4
23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 80? (a) 8 (b) 17 (c) 18 (d) 19
25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 18 (d) 6
26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
27. 27.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
28. 28.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) 30 (b) 10 (c) 33 (d) 90
29. 29.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) 69 (c) 207 (d) 72
30. 30.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 361 (c) 351 (d) 360
31. 31.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) 30 (b) 9 (c) 27 (d) 81
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
33. 33.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) 39 (b) 13 (c) 117 (d) 42
34. 34.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) 45 (c) 15 (d) 5
35. 35.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 490 (c) 489 (d) 480
36. 36.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 469 (d) 468
37. 37.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 444 (b) 435 (c) 445 (d) 368
38. 38.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 363 (c) 364 (d) 314
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 9 (d) 20
40. 40.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) 216 (b) 72 (c) 75 (d) 24

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