Competition · AMC preparation · step 4 of 4
AMC 8 · 2025 · #2
Grade 4 arithmetic
Pick an answer.
AMC 8 2025 problem © Mathematical Association of America (MAA AMC). Reproduced for educational use.
The cleanest path is Tool #2 (Systematic List): walk through the four distinct symbol types from largest value to smallest, tally how many of each appear, and multiply count × value. Because the Egyptian system is additive, the answer is just the sum of these four products — no place-value juggling needed. Tool #3 (Eliminate Possibilities) is a great second pass for multiple-choice: the absence of the lotus flower (1,000) forces the thousands digit to be 0, which alone narrows the five choices down to (B) 10,423, giving us an independent check on our computation.
Count each symbol
Sort the symbols by value, largest first, and count how many of each appear so no group is missed or double-counted.
Sorting objects into the right buckets and counting each bucket is a Kindergarten classify-and-count move.
K.MD.B.3Make A Systematic ListMultiply counts by values
Multiply each count by its symbol's value — a single digit times a power of ten, so just attach the matching number of zeros.
Multiplying a one-digit number by 10, 100, or 10,000 is the Grade 3 "multiples of 10" pattern — just attach the zeros.
3.NBT.A.3Make A Systematic ListAdd the partial values
Add the four partial values — no two share a place, so there are no carries and the total is 10,423.
Fluently adding multi-digit whole numbers up to the ten-thousands place is a Grade 4 standard.
Combining the four symbol groups gives 10,000 + 400 + 20 + 3 = 10,423, with each group's value dropping into its own digit place and nothing to carry.
▸ Why?
Putting the symbol groups together is the same as adding their separate values, because the number is nothing more than all its groups taken together.
▸ Why?
The four groups (bent finger, coiled ropes, heel bones, single strokes) sort every symbol into separate piles with no overlaps, so their values must add back to the whole number.
▸ Why?
The four values 10,000, 400, 20, and 3 each fill a different place column, so they line up side by side and no two digits ever collide.
▸ Why?
400 is four hundreds, 20 is two tens, and 3 is three ones, and each of these columns is a separate power of ten stacked above the last.
Match the total to the choices
Cross-check by elimination — the bent finger means at least 10,000 and no lotus flower forces a 0 in the thousands place, so only (B) fits.
Reading a five-digit number and comparing it to the choices uses Grade 4 multi-digit place-value understanding.
4.NBT.A.2Eliminate PossibilitiesThis AMC 8 problem only needs Grade 4 place value and multi-digit addition you already know!
- Count each symbol
- Multiply counts by values
- Add the partial values
- Match the total to the choices
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