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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 968 · 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.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) 9 (b) 30 (c) 27 (d) 81
  2. 2.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 412 (c) 346 (d) 411
  3. 3.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 546 (c) 556 (d) 442
  4. 4.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 321 (d) 322
  5. 5.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 75 (c) 66 (d) 84
  6. 6.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) 22 (b) 66 (c) 198 (d) 69
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 16 (b) 6 (c) 15 (d) 17
  8. 8.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) 21 (b) 18 (c) 54 (d) 6
  9. 9.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 390 (c) 332 (d) 381
  10. 10.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 328 (c) 318 (d) 327
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  12. 12.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) 153 (b) 17 (c) 54 (d) 51
  13. 13.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 126 (c) 125 (d) 116
  14. 14.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
  15. 15.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 486 (c) 621 (d) 612
  16. 16.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 552 (c) 561 (d) 446
  17. 17.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) 90 (c) 30 (d) 10
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 10 (d) 6
  19. 19.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 16 (b) 15 (c) 17 (d) 5
  21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 18 (b) 19 (c) 9 (d) 20
  22. 22.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 126 (c) 136 (d) 135
  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) 7 (b) 21 (c) 63 (d) 24
  24. 24.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 126 (b) 45 (c) 14 (d) 42
  25. 25.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) 42 (c) 39 (d) 117
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  27. 27.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 643 (c) 642 (d) 500
  28. 28.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 134 (d) 143
  29. 29.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 154 (c) 163 (d) 164
  30. 30.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 165 (b) 156 (c) 166 (d) 174
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 14 (d) 5
  32. 32.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 187 (c) 178 (d) 196
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 8 (b) 7 (c) 9 (d) 6
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 5 (d) 6
  35. 35.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 6 (b) 9 (c) 7 (d) 8
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 42? (a) 14 (b) 15 (c) 16 (d) 4
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 4 (b) 15 (c) 13 (d) 14
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 5 (d) 3

Answer key

  1. 27
  2. 411
  3. 555
  4. 321
  5. 75
  6. 66
  7. 16
  8. 18
  9. 390
  10. 327
  11. 4
  12. 51
  13. 125
  14. 3
  15. 621
  16. 561
  17. 30
  18. 7
  19. 8
  20. 16
  21. 19
  22. 135
  23. 21
  24. 42
  25. 39
  26. 2
  27. 642
  28. 143
  29. 163
  30. 165
  31. 15
  32. 187
  33. 8
  34. 5
  35. 6
  36. 8
  37. 15
  38. 14
  39. 5
  40. 4

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