Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 411 · 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) 4 (c) 17 (d) 3
2. 2.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 44 (c) 54 (d) 62
3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 5 (d) 4
4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 18 (c) 17 (d) 6
5. 5.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) 48 (c) 15 (d) 45
6. 6.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 390 (c) 400 (d) 338
7. 7.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) 42 (c) 13 (d) 39
8. 8.The numbers 17 to 25 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) 66 (d) 189
9. 9.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 325 (c) 288 (d) 315
10. 10.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) 12 (b) 108 (c) 36 (d) 39
11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 19 (b) 17 (c) 18 (d) 8
12. 12.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
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) 20 (b) 60 (c) 63 (d) 180
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 18 (b) 16 (c) 6 (d) 17
15. 15.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 168 (c) 159 (d) 160
16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 18 (b) 20 (c) 19 (d) 9
17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 16 (c) 14 (d) 15
18. 18.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) 5 (c) 15 (d) 45
19. 19.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 114 (c) 132 (d) 123
20. 20.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) 194 (c) 176 (d) 186
21. 21.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 345 (c) 346 (d) 302
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 12 (c) 3 (d) 13
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) 63 (b) 24 (c) 7 (d) 21
24. 24.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) 16 (b) 48 (c) 51 (d) 144
25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 20 (d) 18
26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
27. 27.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 604 (b) 603 (c) 474 (d) 594
28. 28.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) 72 (d) 207
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14
31. 31.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 5 (d) 14
33. 33.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
34. 34.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 177 (c) 186 (d) 168
35. 35.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) 198 (b) 66 (c) 69 (d) 22
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 17 (d) 8
37. 37.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 297 (c) 298 (d) 270
38. 38.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 6 (c) 4 (d) 7
40. 40.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3

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