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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 640 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 6 (d) 10
  3. 3.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
  4. 4.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 58 (c) 50 (d) 49
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 91? (a) 9 (b) 20 (c) 18 (d) 19
  6. 6.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 285 (c) 262 (d) 276
  7. 7.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) 21 (c) 6 (d) 54
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 7 (b) 6 (c) 5 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  11. 11.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) 33 (c) 11 (d) 99
  12. 12.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  13. 13.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) 13 (b) 39 (c) 117 (d) 42
  14. 14.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  15. 15.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) 63 (c) 21 (d) 24
  16. 16.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) 144 (d) 51
  17. 17.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 344 (c) 408 (d) 409
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 7 (b) 8 (c) 6 (d) 9
  19. 19.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 166 (c) 176 (d) 175
  20. 20.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 360 (c) 433 (d) 432
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  22. 22.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 568 (c) 558 (d) 567
  23. 23.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 19 (b) 60 (c) 57 (d) 171
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 4 (d) 2
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 15 (b) 4 (c) 16 (d) 14
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  27. 27.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 285 (c) 268 (d) 295
  28. 28.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 51 (c) 153 (d) 54
  29. 29.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 7 (d) 6
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 6 (b) 8 (c) 7 (d) 9
  33. 33.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 543 (c) 534 (d) 544
  34. 34.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) 60 (b) 20 (c) 63 (d) 180
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  36. 36.The numbers 4 to 12 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) 24 (c) 8 (d) 27
  37. 37.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) 90 (b) 33 (c) 30 (d) 10
  38. 38.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 223 (c) 213 (d) 222
  39. 39.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 8 (d) 11
  40. 40.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 264 (c) 279 (d) 289

Answer key

  1. 7
  2. 6
  3. 69
  4. 49
  5. 19
  6. 285
  7. 18
  8. 17
  9. 7
  10. 2
  11. 33
  12. 6
  13. 39
  14. 2
  15. 21
  16. 48
  17. 408
  18. 8
  19. 175
  20. 432
  21. 3
  22. 567
  23. 57
  24. 3
  25. 15
  26. 3
  27. 294
  28. 51
  29. 5
  30. 4
  31. 7
  32. 8
  33. 543
  34. 60
  35. 5
  36. 24
  37. 30
  38. 222
  39. 9
  40. 288

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