Build around 10
Instead of 47 × 6, think 50 × 6 − 3 × 6. Friendly tens are often quicker to manipulate mentally.
Think in anchors, gaps and repairs
How to get better at number puzzles
A strong numbers-round player is not trying every possible calculation. The useful habit is to build a short list of promising routes: get near the target with a large, easy calculation, measure the gap, then ask whether the remaining tiles can repair it.
The techniques below are useful for SumGoal and for other arithmetic target puzzles in the tradition of the Countdown numbers round. They are not rigid rules; they are patterns that reduce the amount of searching your brain has to do.
1 · AnchorMake a nearby easy number
Often a multiple of 25, 50, 75 or 100.
2 · GapMeasure what is missing
How far above or below the target are you?
3 · RepairUse the remaining tiles
Make the gap with as few useful numbers as possible.
1. Learn the useful large-number multiples
Rachel Riley has described re-learning all her times tables when preparing for her Countdown interview. For the numbers round, one particularly useful extra table is 75 because its multiples land all over the three-digit target range. Competitive Countdown resources repeatedly recommend learning it cold.
75 × 2150
75 × 3225
75 × 4300
75 × 5375
75 × 6450
75 × 7525
75 × 8600
75 × 9675
75 × 10750
75 × 11825
75 × 12900
75 × 13975
75-times-table drill
Build instant recall so these numbers appear as anchors without effort.
75 × 7 = ?
Spot the gap
Train the second half of the anchor method: quickly see how much correction is needed.
675 → 683
How much would you need to add?
2. Work backwards from the target
Instead of combining random tiles and hoping they drift towards the answer, ask which nearby numbers are easy to build. A target of 683 immediately suggests 675 if you know 75 × 9. That leaves a gap of only 8.
75 × 9→675+ 8 →683
This is why knowing a handful of reliable multiples matters: they turn a target that looks arbitrary into a small correction problem.
3. Overshoot on purpose
Getting above the target is not a mistake if the excess is easier to build than the shortfall. A common technique is to choose the nearest convenient multiple and then subtract the difference.
Example: target 273
75 × 4→300− 27 →273
If the remaining tiles are 5, 6, 2 and 1, then 5 × 6 − 2 − 1 = 27. The overshoot gives you a clear subproblem instead of a vague search.
4. Keep small numbers available for repairs
Small tiles are often most valuable late in the solve because they can make precise adjustments. Burning a 1, 2 or 3 too early may leave you stuck one or two away from the target.
Useful habit: if you already have a strong large-number route, ask whether you can postpone using the smallest tiles until you know the final gap.
This is not absolute. Sometimes a small number is exactly what makes a useful multiplier — for example 8 + 1 = 9 before multiplying by 75. The point is to spend small numbers deliberately rather than automatically.
5. Split awkward multiplication into easy pieces
You do not need to know every difficult product if you can rewrite it around a friendly number. The technique is essentially mental distributive multiplication.
Example: target 828
100 × 9→900−8 × 9 = 72→828
If you have 100, 9 and 8, think of 92 × 9 as (100 − 8) × 9. You only need the easy facts 900 and 72.
Build around 100
Numbers such as 98 × 7 become 700 − 14. The closer your factor is to 100, the more useful this becomes.
Use 25 as a quarter of 100
25 × 12 is 300 because 100 × 12 is 1200 and a quarter is 300. The 25 and 75 tables become easier when linked to 100.
Use 75 as three quarters of 100
75 × 8 is three quarters of 800, so 600. This gives another route to recall if the table itself is not automatic yet.
6. Look for factor opportunities before long addition chains
Multiplication can compress several tiles into one powerful move. If two small numbers can make 9, 10, 11 or 12, they may combine naturally with a large tile. Likewise, altering a large number before multiplying can create a surprisingly direct route.
Change the anchor before multiplying
75 − 6→69× 4 →276− 3 →273
This is another way to think about the same target: rather than make 300 and subtract 27, change the 75 before scaling it.
7. Practise recognising structure, not memorising solutions
The best practice is short and repeated. Spend a minute on 75 multiples, a minute spotting gaps to nearby 25/50/75/100 multiples, then play a few full rounds. Over time you start seeing the same structures without consciously calculating every possibility.
A useful five-minute routine: 60 seconds of 75-times-table recall, 60 seconds of gap spotting, then three untimed SumGoal rounds where your only goal is to identify a sensible anchor before making your first move.
Want to put the ideas into practice? Play a round of SumGoal, or use the solver afterwards to compare your route with a short solution.
Sources and further reading
This guide combines general mental-arithmetic methods with techniques widely discussed by Countdown players. Rachel Riley has spoken about re-learning her times tables while preparing for Countdown; established Countdown strategy resources emphasise the 75 table, nearby large-number multiples, overshooting and split multiplication.
SumGoal is an independent game and is not affiliated with or endorsed by Countdown, Channel 4 or any broadcaster.