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Making any amount

Why Do Coins Have Different Values?

A handful of well-chosen values can build any price with very few coins.

1 A few chosenvalues2+Combine them3=Any amount atall
1, 2, 5, 10, 20, 50 — not an accident.

  1. Step 1 of 5

    One coin value would be hopeless.

    Only 1p coins 500 coins for £5Mixed values A handful does it

    If everything were 1p, a £5 purchase would mean carrying five hundred coins. Different values exist to keep your pocket manageable.

  2. Step 2 of 5

    The values follow a 1, 2, 5 pattern.

    Worst case with 1,2,54 coinsWith only 1s and 10sup to 18 coinsWith only 1sup to 99 coins

    1, 2, 5, then 10, 20, 50, then £1 and £2. That spacing lets you build every amount from 1 to 99 using at most four coins.

  3. Step 3 of 5

    Making change is subtraction you can hold.

    1 65p2+Count up: 75,95…3=£1 — so 35pchange

    Pay £1 for a 65p item and you need 35p back. Counting up — 65, 75, 95, £1 — turns the subtraction into easy addition.

  4. Step 4 of 5

    The value is agreed, not physical.

    The metal in a coin Worth almost nothingThe agreement about it Worth its face value

    A £2 coin is not worth twice a £1 coin in metal. Its value comes from everyone agreeing to accept it, which is what money actually is.

  5. Step 5 of 5

    Coins made trade possible at all.

    1 You want bread2 Sell to anyonefor coins3+Buy from anyonewith coins

    Before money you needed someone who had bread and also wanted your shoes. Coins let you sell to one person and buy from another.

    The 1p coin now costs more to make than it is worth. Several countries have simply stopped making theirs.

The short version

Coin values follow a 1-2-5 pattern so that a handful can make any amount, and their value comes from agreement.

Try it yourself

Try making 87p in as few coins as possible. Four is the answer: 50 + 20 + 10 + 5 + 2. Now try with only 1p coins.

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