Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 404 · 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 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) 15 (b) 48 (c) 135 (d) 45
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
3. 3.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
4. 4.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 4 (d) 5
5. 5.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) 144 (b) 51 (c) 16 (d) 48
6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 7 (d) 19
7. 7.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 386 (c) 472 (d) 471
8. 8.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) 81 (b) 9 (c) 27 (d) 30
9. 9.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
10. 10.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 594 (d) 468
11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 6 (b) 8 (c) 7 (d) 9
12. 12.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 4 (d) 5
14. 14.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 110 (c) 118 (d) 100
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.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) 63 (b) 60 (c) 20 (d) 180
17. 17.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) 18 (b) 6 (c) 54 (d) 21
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) 207 (b) 72 (c) 23 (d) 69
19. 19.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 7 (b) 4 (c) 6 (d) 5
21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
22. 22.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 565 (d) 564
23. 23.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 334 (c) 384 (d) 394
24. 24.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) 126 (c) 134 (d) 125
25. 25.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 441 (c) 450 (d) 451
26. 26.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 36 (c) 26 (d) 35
27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 6 (d) 5
28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 4 (b) 15 (c) 16 (d) 14
29. 29.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) 24 (b) 216 (c) 72 (d) 75
30. 30.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 271 (b) 252 (c) 270 (d) 261
31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
32. 32.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 101 (b) 102 (c) 92 (d) 110
33. 33.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 183 (c) 192 (d) 193
34. 34.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 10 (d) 2
35. 35.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
36. 36.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 186 (c) 202 (d) 196
37. 37.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
38. 38.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 128 (c) 137 (d) 138
39. 39.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 129 (c) 138 (d) 120
40. 40.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) 162 (b) 18 (c) 57 (d) 54

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