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Sum finder – find the numbers that add up to a target sum

Find the numbers that add up to a target sum – and the ones that are missing. For reconciliations, invoices and payslip checks.

Sum finder
Find the numbers that add up to a target sum – and the ones that are missing
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About the sum finder

The sum finder looks through a list of numbers for the ones that add up to a specific sum. You paste in the numbers and the target sum, and the tool shows every combination that works. Under each combination are the numbers that are left out. These are often exactly what you are looking for: the missing invoice, the entry that creates the difference, or the pay component that is not included in the pension.

Find which numbers add up to a given sum

Enter the sum in Target sum and paste the numbers with one number per line – for example straight from an Excel column or a bank statement. Click Analyse. The tool tries every combination and shows the ones that hit the sum, closest first.

In Excel this problem can only be solved with the Solver add-in, which needs a helper column and constraints to be set up. Solver also finds just one solution. The sum finder shows all solutions, so you can see whether the numbers can add up in more than one way. Amounts can be pasted in the format you already have: 1,286.00, 1.286,00 and 1 286,00 are all read correctly.

Reconciliation: find the difference you cannot locate

When a reconciliation does not balance, the difference is almost always one or more entries that are missing, appear twice or are posted wrongly. Use the difference as the target sum and the period's entries as the list. The tool shows which entries add up to the difference.

Bank reconciliation – which entries make up the amount?

The bank shows 1,637.50 more than the ledger. The month's entries are 412.50 · 1,225.00 · 89.95 · 2,340.00 · 618.00 · 318.75 · 1,104.25 · 145.00.

412.50 + 1,225.00 = 1,637.50 ✓

Those are the two entries to check in the ledger. Try the example with the Find the difference button at the top.

Receivables: which invoices does the payment cover?

A customer has paid 4,750 without quoting invoice numbers. The open invoices are 1,200 · 850 · 2,700 · 1,450 · 3,250.

1,200 + 850 + 2,700 = 4,750 ✓

Under Not included in the sum you will find 1,450 and 3,250 – the invoices that are still open.

Three rules of thumb when the difference will not add up

  • The difference is divisible by 9: Two digits have probably been transposed. 1,286 keyed in as 1,826 gives a difference of 540 = 9 × 60.
  • Half the difference exists as an entry: Then that entry has been posted with the wrong sign – as income instead of expense or the other way round. Search for the difference divided by 2.
  • Neither: Use the difference as the target sum and the entries as the list. If several combinations add up, check them all.

Payslip check (Denmark): what are pension and the free-choice account based on?

This section is about Danish payslips and collective agreements (overenskomster); the amounts are in Danish kroner (DKK). A payslip usually shows only the pension contribution or the free-choice amount (fritvalgslønkonto) – not which pay components the amount was calculated from. You find the basis by dividing the amount by the rate. Use the basis as the target sum and the payslip's pay components as the list. The tool shows which components are included and which are not. Use an allowed deviation of 1–2 DKK, because the amounts are rounded to whole øre.

Example: is overtime pensionable?

The company pension is 8% = DKK 2,522.91. The basis is 2,522.91 / 0.08 = DKK 31,536.38. The pay components are basic salary 28,450.00 · personal supplement 1,850.00 · unsocial-hours allowance (genetillæg) 1,236.40 · overtime 2,114.60.

28,450.00 + 1,850.00 + 1,236.40 = 31,536.40 ✓

Overtime appears under Not included in the sum, so it is not part of the pension basis. Try the example with the Check pension basis button.

Example: the basis of the free-choice pay account

The free-choice pay account (fritvalgslønkonto) is 4% = DKK 1,198.00. The basis is 1,198.00 / 0.04 = DKK 29,950.00. The pay components are basic salary 28,100.00 · supplement 1,850.00 · unsocial-hours allowance 1,236.40 · overtime 2,114.60.

28,100.00 + 1,850.00 = 29,950.00 ✓

The unsocial-hours allowance and overtime are not included. Use the rate from your own payslip – it depends on the collective agreement.

You can work out the rate with the percentage calculator if the payslip shows only the amount. To check the rest of the pay, use the salary conversion calculator or the real wage calculator.

What is counted?
  • Exact match: All combinations that hit the target sum to the cent.
  • Deviation: With an allowed deviation as an amount or a percentage, combinations close to the target sum are included too – useful for rounding, fees and currency conversion.
  • Omitted numbers: Under each combination are the numbers that are not part of it, together with their total.
  • Max. 20 numbers: 20 numbers give over 1 million combinations, and the limit keeps the calculation fast in the browser.
The fields explained
  • Target sum: The amount the numbers should add up to – a payment, a difference or a calculation basis.
  • Allowed deviation: How far the sum may differ from the target sum. Enter 0 for an exact match.
  • Numbers to analyse: One number per line. 1286.00, 1,286.00, 1.286,00 and 1 286,00 are read as the same amount, and the minus sign can come before or after the number.
  • Results: The ten closest combinations, sorted by deviation.

Worked examples

Payment against open invoices

Target sum 4,750, deviation 0. Invoices: 1,200, 850, 2,700, 1,450, 3,250.

1,200 + 850 + 2,700 = 4,750 ✓

Not included in the sum:1,450 and 3,250

Pension basis with a deviation

Target sum 31,536.38, deviation 1. Pay components: 28,450.00, 1,850.00, 1,236.40, 2,114.60.

28,450.00 + 1,850.00 + 1,236.40 = 31,536.40 ✓ (deviation 0.02)

Not included in the sum:Overtime 2,114.60
As an employer, keep in mind

A mathematical match is not proof. If several combinations add up, check the vouchers before you clear or correct an entry.

If you have more than 20 entries, split the reconciliation up – for example by week or by customer – and look for partial sums.

As an employee, keep in mind

Which pay components are pensionable or count towards the free-choice pay account is set out in your collective agreement or contract. The tool shows what has actually been included – compare it with the agreement.

If you find a pay component that should have been included, take the payslip to your shop steward or your trade union.

Questions and answers

How do I find which numbers add up to a specific sum?

Enter the sum as the target sum and paste in the numbers, one per line. The tool tries every combination and shows the ones that add up – and the numbers that are left out.

Can Excel find which numbers add up to a given sum?

Yes, with the Solver add-in, but it needs a helper column and constraints to be set up, and it finds only one solution. Here you paste in the column and see all the solutions.

How do I find a difference in a reconciliation?

Use the difference as the target sum and the period's entries as the list. If the difference is divisible by 9, two digits have probably been transposed. If half the difference exists as an entry, it has been posted with the wrong sign.

How can I see what my pension is calculated from?

Divide the pension contribution on the payslip by the rate – for example 2,522.91 / 0.08 = 31,536.38 DKK. Use the result as the target sum and the pay components as the list, with 1 DKK of allowed deviation. The components under "Not included in the sum" are not part of the basis. This applies to Danish payslips and collective agreements.

Why can I only enter 20 numbers?

The number of combinations doubles with every number. 20 numbers give over 1 million combinations, which the browser can work through in an instant. If you have more numbers, split the list and look for partial sums.

Are my numbers stored by UniteApps?

No. The calculation runs in your browser, and the numbers never leave your computer.

Content last reviewed October 2026.